Search results for: Nonlinear equations

Authors: Beata Jackowska-Zduniak

Abstract:

We formulate and analyze a mathematical model describing dynamics of the hypothalamus-pituitary-thyroid homoeostatic mechanism in endocrine system. We introduce to this system two types of couplings and delay. In our model, feedback controls the secretion of thyroid hormones and delay reflects time lags required for transportation of the hormones. The influence of delayed feedback on the stability behaviour of the system is discussed. Analytical results are illustrated by numerical examples of the model dynamics. This system of equations describes normal activity of the thyroid and also a couple of types of malfunctions (e.g. hyperthyroidism).

Keywords: Mathematical modeling, ordinary differential equations, endocrine system, stability analysis.

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Authors: Anuar Ishak

Abstract:

The mixed convection stagnation point flow toward a vertical plate is investigated. The external flow impinges normal to the heated plate and the surface temperature is assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the mixed convection parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: Dual solutions, heat transfer, mixed convection, stability analysis.

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Authors: M. Palizvan, M. T. Abadi, M. H. Sadr

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Due to variations in damage mechanisms in the microscale, the behavior of fiber-reinforced composites is nonlinear and difficult to model. To make use of computational advantages, homogenization method is applied to the micro-scale model in order to minimize the cost at the expense of detail of local microscale phenomena. In this paper, the effective stiffness is calculated using the homogenization of nonlinear behavior of a composite representative volume element (RVE) containing fiber-matrix debonding. The damage modes for the RVE are considered by using cohesive elements and contacts for the cohesive behavior of the interface between fiber and matrix. To predict more realistic responses of composite materials, different random distributions of fibers are proposed besides square and hexagonal arrays. It was shown that in some cases, there is quite different damage behavior in different fiber distributions. A comprehensive comparison has been made between different graphs.

Keywords: Homogenization, cohesive zone model, fiber-matrix debonding, RVE.

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Authors: R. Bhargava, Sonam Singh

Abstract:

In the present study, a numerical analysis is carried out to investigate unsteady MHD (magneto-hydrodynamic) flow and heat transfer of a non-Newtonian second grade viscoelastic fluid over an oscillatory stretching sheet. The flow is induced due to an infinite elastic sheet which is stretched oscillatory (back and forth) in its own plane. Effect of viscous dissipation and joule heating are taken into account. The non-linear differential equations governing the problem are transformed into system of non-dimensional differential equations using similarity transformations. A newly developed meshfree numerical technique Element free Galerkin method (EFGM) is employed to solve the coupled non linear differential equations. The results illustrating the effect of various parameters like viscoelastic parameter, Hartman number, relative frequency amplitude of the oscillatory sheet to the stretching rate and Eckert number on velocity and temperature field are reported in terms of graphs and tables. The present model finds its application in polymer extrusion, drawing of plastic films and wires, glass, fiber and paper production etc.

Keywords: EFGM, MHD, Oscillatory stretching sheet, Unsteady, Viscoelastic

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Authors: Rafael Jorge Menezes Santos, Ginalber Luiz de Oliveira Serra, Carlos César Teixeira Ferreira

Abstract:

This paper proposes a methodology for analysis of the dynamic behavior of a robotic manipulator in continuous time. Initially this system (nonlinear system) will be decomposed into linear submodels and analyzed in the context of the Linear and Parameter Varying (LPV) Systems. The obtained linear submodels, which represent the local dynamic behavior of the robotic manipulator in some operating points were grouped in a Takagi-Sugeno fuzzy structure. The obtained fuzzy model was analyzed and validated through analog simulation, as universal approximator of the robotic manipulator.

Keywords: modeling of nonlinear dynamic systems, Takagi- Sugeno fuzzy model, Linear and Parameter Varying (LPV) System.

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Authors: A. Khelassi, R. Bendib

Abstract:

The paper considers the effect of feed plate location on the interactions in a seven plate binary distillation column. The mathematical model of the distillation column is deduced based on the equations of mass and energy balances for each stage, detailed model for both reboiler and condenser, and heat transfer equations. The Dynamic Relative Magnitude Criterion, DRMC is used to assess the interactions in different feed plate locations for a seven plate (Benzene-Toluene) binary distillation column ( the feed plate is originally at stage 4). The results show that whenever we go far from the optimum feed plate position, the level of interaction augments.

Keywords: Distillation column, assessment of interactions, feedplate location, DRMC.

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Authors: O. A. Akinfenwa, N.M. Yao, S. N. Jator

Abstract:

In this paper, a self starting two step continuous block hybrid formulae (CBHF) with four Off-step points is developed using collocation and interpolation procedures. The CBHF is then used to produce multiple numerical integrators which are of uniform order and are assembled into a single block matrix equation. These equations are simultaneously applied to provide the approximate solution for the stiff ordinary differential equations. The order of accuracy and stability of the block method is discussed and its accuracy is established numerically.

Keywords: Collocation and Interpolation, Continuous HybridBlock Formulae, Off-Step Points, Stability, Stiff ODEs.

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Authors: Atul Krishna Banik

Abstract:

Nonlinear response behaviour of a cracked RC beam under harmonic excitation is analysed to investigate various instability phenomena like, bifurcation, jump phenomena etc. The nonlinearity of the system arises due to opening and closing of the cracks in the RC beam and is modelled as a cubic polynomial. In order to trace different branches at the bifurcation point on the response curve (amplitude versus frequency of excitation plot), an arc length continuation technique along with the incremental harmonic balance (IHBC) method is employed. The stability of the solution is investigated by the Floquet theory using Hsu-s scheme. The periodic solutions obtained by the IHBC method are compared with these obtained by the numerical integration of the equation of motion. Characteristics of solutions fold bifurcation, jump phenomena and from stable to unstable zones are identified.

Keywords: Incremental harmonic balance, arc-length continuation, bifurcation, jump phenomena.

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Authors: Praloy Kumar Biswas, Prof. Dipanwita Roy Chowdhury

Abstract:

Grobner basis calculation forms a key part of computational commutative algebra and many other areas. One important ramification of the theory of Grobner basis provides a means to solve a system of non-linear equations. This is why it has become very important in the areas where the solution of non-linear equations is needed, for instance in algebraic cryptanalysis and coding theory. This paper explores on a parallel-distributed implementation for Grobner basis calculation over GF(2). For doing so Buchberger algorithm is used. OpenMP and MPI-C language constructs have been used to implement the scheme. Some relevant results have been furnished to compare the performances between the standalone and hybrid (parallel-distributed) implementation.

Keywords: Grobner basis, Buchberger Algorithm, Distributed- Parallel Computation, OpenMP, MPI.

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Authors: Mohammed Sabri Ali Akresh

Abstract:

The modern technologies and developments in computer and Global Positioning System (GPS) as well as Geographic Information System (GIS) and total station TS. This paper presents a new proposal for coordinates system by a harmonic equations “United projections”, which have five projections (Mercator, Lambert, Russell, Lagrange, and compound of projection) in one zone coordinate system width 14 degrees, also it has one degree for overlap between zones, as well as two standards parallels for zone from 10 S to 45 S. Also this paper presents two cases; first case is to compare distances between a new coordinate system and UTM, second case creating local coordinate system for the city of Sydney to measure the distances directly from rectangular coordinates using projection of Mercator, Lambert and UTM.

Keywords: Harmonic equations, coordinate system, projections, algorithms and parallels.

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Authors: A.Roshandel, N.Hedayat, H.kiamanesh

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Today, numerical simulation is a powerful tool to solve various hydraulic engineering problems. The aim of this research is numerical solutions of shallow water equations using finite volume method for Simulations of dam break over wet and dry bed. In order to solve Riemann problem, Roe-s approximate solver is used. To evaluate numerical model, simulation was done in 1D and 2D states. In 1D state, two dam break test over dry bed (with and without friction) were studied. The results showed that Structural failure around the dam and damage to the downstream constructions in bed without friction is more than friction bed. In 2D state, two tests for wet and dry beds were done. Generally in wet bed case, waves are propagated to canal sides but in dry bed it is not significant. Therefore, damage to the storage facilities and agricultural lands in wet bed case is more than in dry bed.

Keywords: dam break, dry bed, finite volume method, shallow water equations.

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Authors: P. Ramana , K. Alice Mary, M. Surya Kalavathi, M. Phani Kumar

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This paper discusses two observers, which are used for the estimation of parameters of PMSM. Former one, reduced order observer, which is used to estimate the inaccessible parameters of PMSM. Later one, full order observer, which is used to estimate all the parameters of PMSM even though some of the parameters are directly available for measurement, so as to meet with the insensitivity to the parameter variation. However, the state space model contains some nonlinear terms i.e. the product of different state variables. The asymptotic state observer, which approximately reconstructs the state vector for linear systems without uncertainties, was presented by Luenberger. In this work, a modified form of such an observer is used by including a non-linear term involving the speed. So, both the observers are designed in the framework of nonlinear control; their stability and rate of convergence is discussed.

Keywords: Permanent magnet synchronous motor, Mathematicalmodelling, Rotor reference frame, parameter estimation, Luenbergerobserver, reduced order observer, full order observer

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Authors: Giovanni Incerti

Abstract:

In this paper the vibration of a synchronous belt drive during start-up is analyzed and discussed. Besides considering the belt elasticity, the model here proposed also takes into consideration the electromagnetic response of the DC motor. The solution of the motion equations is obtained by means of the modal analysis in state space, which allows to obtain the decoupling of all equations, without introducing the hypothesis of proportional damping. The mathematical model of the transmission and the solution algorithms have been implemented within a computing software that allows the user to simulate the dynamics of the system and to evaluate the effects due to the elasticity of the belt branches and to the electromagnetic behavior of the DC motor. In order to show the details of the calculation procedure, the paper presents a case study developed with the aid of the above-mentioned software.

Keywords: Belt drive, Vibrations, Startup, DC motor.

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Authors: M. G. Murtaza, E. E. Tzirtzilakis, M. Ferdows

Abstract:

The mixed convective flow of MHD incompressible, steady boundary layer in heat transfer over a curved stretching sheet due to temperature dependent thermal conductivity is studied. We use curvilinear coordinate system in order to describe the governing flow equations. Finite difference solutions with central differencing have been used to solve the transform governing equations. Numerical results for the flow velocity and temperature profiles are presented as a function of the non-dimensional curvature radius. Skin friction coefficient and local Nusselt number at the surface of the curved sheet are discussed as well.

Keywords: Curved stretching sheet, finite difference method, MHD, variable thermal conductivity.

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Authors: Eda Gök

Abstract:

Peridynamics is a new modeling concept of non-local interactions for solid structures. The formulations of Peridynamic (PD) theory are based on integral equations rather than differential equations. Through, undefined equations of associated problems are avoided. PD theory might be defined as continuum version of molecular dynamics. The medium is usually modeled with mass particles bonded together. Particles interact with each other directly across finite distances through central forces named as bonds. The main assumption of this theory is that the body is composed of material points which interact with other material points within a finite distance. Although, PD theory developed for discontinuities, it gives good results for structures which have no discontinuities. In this paper, displacement control of the isotropic plate under the effect of tensile and bending loading has been investigated by means of PD theory. A MATLAB code is generated to create PD bonds and corresponding surface correction factors. Using generated MATLAB code the geometry of the specimen is generated, and the code is implemented in Finite Element Software. The results obtained from non-local continuum theory are compared with the Finite Element Analysis results and analytical solution. The results show good agreement.

Keywords: Flexural loading, non-local continuum mechanics, Peridynamic theory, solid structures, tensile loading.

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Authors: Atilla Bayram

Abstract:

This paper presents the trajectory tracking control of a spatial redundant hybrid manipulator. This manipulator consists of two parallel manipulators which are a variable geometry truss (VGT) module. In fact, each VGT module with 3-degress of freedom (DOF) is a planar parallel manipulator and their operational planes of these VGT modules are arranged to be orthogonal to each other. Also, the manipulator contains a twist motion part attached to the top of the second VGT module to supply the missing orientation of the endeffector. These three modules constitute totally 7-DOF hybrid (parallel-parallel) redundant spatial manipulator. The forward kinematics equations of this manipulator are obtained, then, according to these equations, the inverse kinematics is solved based on an optimization with the joint limit avoidance. The dynamic equations are formed by using virtual work method. In order to test the performance of the redundant manipulator and the controllers presented, two different desired trajectories are followed by using the computed force control method and a switching control method. The switching control method is combined with the computed force control method and genetic algorithm. In the switching control method, the genetic algorithm is only used for fine tuning in the compensation of the trajectory tracking errors.

Keywords: Computed force control method, genetic algorithm, hybrid manipulator, inverse kinematics of redundant manipulators, variable geometry truss.

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Authors: Zilong Feng, Hong Li, Yang Liu, Siriguleng He

Abstract:

In this article, an adaptive least-squares mixed finite element method is studied for pseudo-parabolic integro-differential equations. The solutions of least-squares mixed weak formulation and mixed finite element are proved. A posteriori error estimator is constructed based on the least-squares functional and the posteriori errors are obtained.

Keywords: Pseudo-parabolic integro-differential equation, least squares mixed finite element method, adaptive method, a posteriori error estimates.

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Authors: S.C. Chin, N. Shafiq, M.F. Nuruddin

Abstract:

To date, theoretical studies concerning the Carbon Fiber Reinforced Polymer (CFRP) strengthening of RC beams with openings have been rather limited. In addition, various numerical analyses presented so far have effectively simulated the behaviour of solid beam strengthened by FRP material. In this paper, a two dimensional nonlinear finite element analysis is presented to validate against the laboratory test results of six RC beams. All beams had the same rectangular cross-section geometry and were loaded under four point bending. The crack pattern results of the finite element model show good agreement with the crack pattern of the experimental beams. The load midspan deflection curves of the finite element models exhibited a stiffer result compared to the experimental beams. The possible reason may be due to the perfect bond assumption used between the concrete and steel reinforcement.

Keywords: CFRP, large opening, RC beam, strengthening

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Authors: M. A. Torkamani, S. Mahmoodzadeh, S. Pourroostaei, C. Lucas

Abstract:

Daily production of information and importance of the sequence of produced data in forecasting future performance of market causes analysis of data behavior to become a problem of analyzing time series. But time series that are very complicated, usually are random and as a result their changes considered being unpredictable. While these series might be products of a deterministic dynamical and nonlinear process (chaotic) and as a result be predictable. Point of Chaotic theory view, complicated systems have only chaotically face and as a result they seem to be unregulated and random, but it is possible that they abide by a specified math formula. In this article, with regard to test of strange attractor and biggest Lyapunov exponent probability of chaos on several foreign exchange rates vs. IRR (Iranian Rial) has been investigated. Results show that data in this market have complex chaotic behavior with big degree of freedom.

Keywords: Chaos, Exchange Rate, Nonlinear Models.

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Authors: Masato Sasaki, Masayoshi Yamamoto

Abstract:

The majority of wireless power transfer (WPT) systems transfer power in a directional manner. This paper describes a discrete exciting voltage control technique for WPT via magnetic resonant coupling with two orthogonal transmitter coils (2D omni-directional WPT system) which can maximize the power transfer efficiency in response to the change of coupling status. The theory allows the equations of the efficiency of the system to be determined at all the rate of the mutual inductance. The calculated results are included to confirm the advantage to one directional WPT system and the validity of the theory and the equations.

Keywords: Wireless power transfer, orthogonal, omni-directional, efficiency.

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Authors: Abdul Rahman Mohd Kasim, Mohd Ariff Admon, Sharidan Shafie

Abstract:

The present paper considers the steady free convection boundary layer flow of a viscoelastics fluid with constant temperature in the presence of heat generation. The boundary layer equations are an order higher than those for the Newtonian (viscous) fluid and the adherence boundary conditions are insufficient to determine the solution of these equations completely. The governing boundary layer equations are first transformed into non-dimensional form by using special dimensionless group. Computations are performed numerically by using Keller-box method by augmenting an extra boundary condition at infinity and the results are displayed graphically to illustrate the influence of viscoelastic K, heat generation γ , and Prandtl Number, Pr parameters on the velocity and temperature profiles. The results of the surface shear stress in terms of the local skin friction and the surface rate of heat transfer in terms of the local Nusselt number for a selection of the heat generation parameterγ (=0.0, 0.2, 0.5, 0.8, 1.0) are obtained and presented in both tabular and graphical formats. Without effect of the internal heat generation inside the fluid domain for which we take γ = 0.0, the present numerical results show an excellent agreement with previous publication.

Keywords: Free Convection, Boundary Layer, CircularCylinder, Viscoelastic Fluid, Heat Generation

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Authors: G. Khamooshian

Abstract:

One of the main points of application of the mechanisms of the series and parallel is the subject of managing them. The control of this mechanism and similar mechanisms is one that has always been the intention of the scholars. On the other hand, modeling the behavior of the system is difficult due to the large number of its parameters, and it leads to complex equations that are difficult to solve and eventually difficult to control. In this paper, a six-linkage robot has been presented that could be used in different areas such as medical robots. Using these robots needs a robust control. In this paper, the system equations are first found, and then the system conversion function is written. A new controller has been designed for this robot which could be used in other parallel robots and could be very useful. Parallel robots are so important in robotics because of their stability, so methods for control of them are important and the robust controller, especially in parallel robots, makes a sense.

Keywords: 3-RRS, 6 linkage, parallel robot, control.

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Authors: Vai Kuong Sin

Abstract:

Non-isothermal stagnation-point flow with consideration of thermal radiation is studied numerically. A set of partial differential equations that governing the fluid flow and energy is converted into a set of ordinary differential equations which is solved by Runge-Kutta method with shooting algorithm. Dimensionless wall temperature gradient and temperature boundary layer thickness for different combinaton of values of Prandtl number Pr and radiation parameter NR are presented graphically. Analyses of results show that the presence of thermal radiation in the stagnation-point flow is to increase the temperature boundary layer thickness and decrease the dimensionless wall temperature gradient.

Keywords: Stagnation-point flow, Similarity solution, Thermal radiation.

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Authors: M. E. Abou-Hashem El Dib, M. K. Swailem, M. M. Metwally, A. I. El Awady

Abstract:

The present work illustrates a parametric study for the effect of stiffeners on the performance of slender built up steel I-columns. To achieve the desired analysis, finite element technique is used to develop nonlinear three-dimensional models representing the investigated columns. The finite element program (ANSYS 13.0) is used as a calculation tool for the necessary nonlinear analysis. A validation of the obtained numerical results is achieved. The considered parameters in the study are the column slenderness ratio and the horizontal stiffener's dimensions as well as the number of stiffeners. The dimensions of the stiffeners considered in the analysis are the stiffener width and the stiffener thickness. Numerical results signify a considerable effect of stiffeners on the performance and failure load of slender built up steel I-columns.

Keywords: Steel I-columns, local buckling, slender, stiffener, thin walled section.

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Authors: Hamid Ahmadi, Shadi Asoodeh

Abstract:

The fatigue life of tubular joints commonly found in offshore industry is not only dependent on the value of hot-spot stress (HSS), but is also significantly influenced by the through-thethickness stress distribution characterized by the degree of bending (DoB). The determination of DoB values in a tubular joint is essential for improving the accuracy of fatigue life estimation using the stresslife (S–N) method and particularly for predicting the fatigue crack growth based on the fracture mechanics (FM) approach. In the present paper, data extracted from finite element (FE) analyses of tubular KT-joints, verified against experimental data and parametric equations, was used to investigate the effects of geometrical parameters on DoB values at the crown 0°, saddle, and crown 180° positions along the weld toe of central brace in tubular KT-joints subjected to axial loading. Parametric study was followed by a set of nonlinear regression analyses to derive DoB parametric formulas for the fatigue analysis of KT-joints under axial loads. The tubular KTjoint is a quite common joint type found in steel offshore structures. However, despite the crucial role of the DoB in evaluating the fatigue performance of tubular joints, this paper is the first attempt to study and formulate the DoB values in KT-joints.

Keywords: Tubular KT-joint, fatigue, degree of bending (DoB), axial loading, parametric formula.

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Authors: R. Simutis, V. Galvanauskas, D. Levisauskas, J. Repsyte, V. Grincas

Abstract:

This paper deals with advanced state estimation algorithms for estimation of biomass concentration and specific growth rate in a typical fed-batch biotechnological process. This biotechnological process was represented by a nonlinear mass-balance based process model. Extended Kalman Filter (EKF) and Particle Filter (PF) was used to estimate the unmeasured state variables from oxygen uptake rate (OUR) and base consumption (BC) measurements. To obtain more general results, a simplified process model was involved in EKF and PF estimation algorithms. This model doesn’t require any special growth kinetic equations and could be applied for state estimation in various bioprocesses. The focus of this investigation was concentrated on the comparison of the estimation quality of the EKF and PF estimators by applying different measurement noises. The simulation results show that Particle Filter algorithm requires significantly more computation time for state estimation but gives lower estimation errors both for biomass concentration and specific growth rate. Also the tuning procedure for Particle Filter is simpler than for EKF. Consequently, Particle Filter should be preferred in real applications, especially for monitoring of industrial bioprocesses where the simplified implementation procedures are always desirable.

Keywords: Biomass concentration, Extended Kalman Filter, Particle Filter, State estimation, Specific growth rate.

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Authors: A. N. K. Nasir, R. M. T. Raja Ismail, M. A. Ahmad

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The objective of this paper is to compare the time specification performance between conventional controller PID and modern controller SMC for an inverted pendulum system. The goal is to determine which control strategy delivers better performance with respect to pendulum-s angle and cart-s position. The inverted pendulum represents a challenging control problem, which continually moves toward an uncontrolled state. Two controllers are presented such as Sliding Mode Control (SMC) and Proportional- Integral-Derivatives (PID) controllers for controlling the highly nonlinear system of inverted pendulum model. Simulation study has been done in Matlab Mfile and simulink environment shows that both controllers are capable to control multi output inverted pendulum system successfully. The result shows that Sliding Mode Control (SMC) produced better response compared to PID control strategies and the responses are presented in time domain with the details analysis.

Keywords: SMC, PID, Inverted Pendulum System.

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Authors: I. A. Farhat

Abstract:

The The dynamic economic dispatch (DED) problem is one of the complex constrained optimization problems that have nonlinear, con-convex and non-smooth objective functions. The purpose of the DED is to determine the optimal economic operation of the committed units while meeting the load demand. Associated to this constrained problem there exist highly nonlinear and non-convex practical constraints to be satisfied. Therefore, classical and derivative-based methods are likely not to converge to an optimal or near optimal solution to such a dynamic and large-scale problem. In this paper, an Artificial Immune System technique (AIS) is implemented and applied to solve the DED problem considering the transmission power losses and the valve-point effects in addition to the other operational constraints. To demonstrate the effectiveness of the proposed technique, two case studies are considered. The results obtained using the AIS are compared to those obtained by other methods reported in the literature and found better.

Keywords: Artificial Immune System (AIS), Dynamic Economic Dispatch (DED).

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Authors: Sohrab Mahmoodi, Ali Rahimi

Abstract:

The critical period for weed control (CPWC) is the period in the crop growth cycle during which weeds must be controlled to prevent unacceptable yield losses. Field studies were conducted in 2005 and 2006 in the University of Birjand at the south east of Iran to determine CPWC of corn using a randomized complete block design with 14 treatments and four replications. The treatments consisted of two different periods of weed interference, a critical weed-free period and a critical time of weed removal, were imposed at V3, V6, V9, V12, V15, and R1 (based on phonological stages of corn development) with a weedy check and a weed-free check. The CPWC was determined with the use of 2.5, 5, 10, 15 and 20% acceptable yield loss levels by non-linear Regression method and fitting Logistic and Gompertz nonlinear equations to relative yield data. The CPWC of corn was from 5- to 15-leaf stage (19-55 DAE) to prevent yield losses of 5%. This period to prevent yield losses of 2.5, 10 and 20% was 4- to 17-leaf stage (14-59 DAE), 6- to 12-leaf stage (25-47 DAE) and 8- to 9-leaf stage (31-36 DAE) respectively. The height and leaf area index of corn were significantly decreased by weed competition in both weed free and weed infested treatments (P<0.01). Results also showed that there was a significant positive correlation between yield and LAI of corn at silk stage when competing with weeds (r= 0.97).

Keywords: Corn, Critical period, Gompertz, Logistic, Weed control.

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Authors: M.A.Behrang, M. Ghalambaz, E. Assareh, A.R. Noghrehabadi

Abstract:

Fluid flow and heat transfer of vertical full cone embedded in porous media is studied in this paper. Nonlinear differential equation arising from similarity solution of inverted cone (subjected to wall temperature boundary conditions) embedded in porous medium is solved using a hybrid neural network- particle swarm optimization method. To aim this purpose, a trial solution of the differential equation is defined as sum of two parts. The first part satisfies the initial/ boundary conditions and does contain an adjustable parameter and the second part which is constructed so as not to affect the initial/boundary conditions and involves adjustable parameters (the weights and biases) for a multi-layer perceptron neural network. Particle swarm optimization (PSO) is applied to find adjustable parameters of trial solution (in first and second part). The obtained solution in comparison with the numerical ones represents a remarkable accuracy.

Keywords: Porous Media, Ordinary Differential Equations (ODE), Particle Swarm Optimization (PSO), Neural Network (NN).

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