Search results for: inverse technique

Authors: A. M. Nazari, B. Sepehrian, M. Jabari

Abstract:

In this paper we study the inverse eigenvalue problem for symmetric special matrices and introduce sufficient conditions for obtaining nonnegative matrices. We get the HROU algorithm from [1] and introduce some extension of this algorithm. If we have some eigenvectors and associated eigenvalues of a matrix, then by this extension we can find the symmetric matrix that its eigenvalue and eigenvectors are given. At last we study the special cases and get some remarkable results.

Keywords: Householder matrix, nonnegative matrix, Inverse eigenvalue problem.

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Authors: Jan Kočí, Jiří Maděra, Miloš Jerman, Robert Černý

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The current practice of determination of moisture diffusivity of building materials under laboratory conditions is predominantly aimed at the absorption phase. The main reason is the simplicity of the inverse analysis of measured moisture profiles. However, the liquid moisture transport may exhibit significant hysteresis. Thus, the moisture diffusivity should be different in the absorption (wetting) and desorption (drying) phase. In order to bring computer simulations of hygrothermal performance of building materials closer to the reality, it is then necessary to find new methods for inverse analysis which could be used in the desorption phase as well. In this paper we present genetic algorithm as a possible method of solution of the inverse problem of moisture transport in desorption phase. Its application is demonstrated for AAC as a typical building material.

Keywords: autoclaved aerated concrete, desorption, genetic algorithm, inverse analysis

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Authors: Sorawit Stapornchaisit, Sidshchadhaa Aumted, Hiroshi Takami

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In this paper, we propose a novel adaptive voltage control strategy for boost converter via Inverse LQ Servo-Control. Our presented strategy is based on an analytical formula of Inverse Linear Quadratic (ILQ) design method, which is not necessary to solve Riccati’s equation directly. The optimal and adaptive controller of the voltage control system is designed. The stability and the robust control are analyzed. Whereas, we can get the analytical solution for the optimal and robust voltage control is achieved through the natural angular velocity within a single parameter and we can change the responses easily via the ILQ control theory. Our method provides effective results as the stable responses and the response times are not drifted even if the condition is changed widely.

Keywords: Boost converter, optimal voltage control, inverse LQ design method, type-1 servo-system, adaptive control.

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Authors: Abdolali Basiri

Abstract:

In this paper we present an efficient method for inverting an ideal in the ideal class group of a Cab curve by extending the method which is presented in [3]. More precisely we introduce a useful generator for the inverse ideal as a K[X]-module.

Keywords: Cab Curves, Ideal Class Group

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Authors: Jieer Wu, Zheshu Ma

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Nondestructive testing in engineering is an inverse Cauchy problem for Laplace equation. In this paper the problem of nondestructive testing is expressed by a Laplace-s equation with third-kind boundary conditions. In order to find unknown values on the boundary, the method of fundamental solution is introduced and realized. Because of the ill-posedness of studied problems, the TSVD regularization technique in combination with L-curve criteria and Generalized Cross Validation criteria is employed. Numerical results are shown that the TSVD method combined with L-curve criteria is more efficient than the TSVD method combined with GCV criteria. The abstract goes here.

Keywords: ill-posed, TSVD, Laplace's equation, inverse problem, L-curve, Generalized Cross Validation.

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Authors: Y. N. Phang, E. F. Loh

Abstract:

Many researchers have suggested the use of zero inflated Poisson (ZIP) and zero inflated negative binomial (ZINB) models in modeling overdispersed medical count data with extra variations caused by extra zeros and unobserved heterogeneity. The studies indicate that ZIP and ZINB always provide better fit than using the normal Poisson and negative binomial models in modeling overdispersed medical count data. In this study, we proposed the use of Zero Inflated Inverse Trinomial (ZIIT), Zero Inflated Poisson Inverse Gaussian (ZIPIG) and zero inflated strict arcsine models in modeling overdispered medical count data. These proposed models are not widely used by many researchers especially in the medical field. The results show that these three suggested models can serve as alternative models in modeling overdispersed medical count data. This is supported by the application of these suggested models to a real life medical data set. Inverse trinomial, Poisson inverse Gaussian and strict arcsine are discrete distributions with cubic variance function of mean. Therefore, ZIIT, ZIPIG and ZISA are able to accommodate data with excess zeros and very heavy tailed. They are recommended to be used in modeling overdispersed medical count data when ZIP and ZINB are inadequate.

Keywords: Zero inflated, inverse trinomial distribution, Poisson inverse Gaussian distribution, strict arcsine distribution, Pearson’s goodness of fit.

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Authors: Minghui Wang, Shanrui Hu

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An inverse problem of doubly center matrices is discussed. By translating the constrained problem into unconstrained problem, two iterative methods are proposed. A numerical example illustrate our algorithms.

Keywords: doubly center matrix, electric network theory, iterative methods, least-square problem.

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Authors: Maatoug Hassine, Mourad Hrizi

Abstract:

In this paper, we consider a geometric inverse source problem for the heat equation with Dirichlet and Neumann boundary data. We will reconstruct the exact form of the unknown source term from additional boundary conditions. Our motivation is to detect the location, the size and the shape of source support. We present a one-shot algorithm based on the Kohn-Vogelius formulation and the topological gradient method. The geometric inverse source problem is formulated as a topology optimization one. A topological sensitivity analysis is derived from a source function. Then, we present a non-iterative numerical method for the geometric reconstruction of the source term with unknown support using a level curve of the topological gradient. Finally, we give several examples to show the viability of our presented method.

Keywords: Geometric inverse source problem, heat equation, topological sensitivity, topological optimization, Kohn-Vogelius formulation.

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Authors: Mingren Shi, Michael Renton

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There is a world-wide need for the development of sustainable management strategies to control pest infestation and the development of phosphine (PH3) resistance in lesser grain borer (Rhyzopertha dominica). Computer simulation models can provide a relatively fast, safe and inexpensive way to weigh the merits of various management options. However, the usefulness of simulation models relies on the accurate estimation of important model parameters, such as mortality. Concentration and time of exposure are both important in determining mortality in response to a toxic agent. Recent research indicated the existence of two resistance phenotypes in R. dominica in Australia, weak and strong, and revealed that the presence of resistance alleles at two loci confers strong resistance, thus motivating the construction of a two-locus model of resistance. Experimental data sets on purified pest strains, each corresponding to a single genotype of our two-locus model, were also available. Hence it became possible to explicitly include mortalities of the different genotypes in the model. In this paper we described how we used two generalized linear models (GLM), probit and logistic models, to fit the available experimental data sets. We used a direct algebraic approach generalized inverse matrix technique, rather than the traditional maximum likelihood estimation, to estimate the model parameters. The results show that both probit and logistic models fit the data sets well but the former is much better in terms of small least squares (numerical) errors. Meanwhile, the generalized inverse matrix technique achieved similar accuracy results to those from the maximum likelihood estimation, but is less time consuming and computationally demanding.

Keywords: mortality estimation, probit models, logistic model, generalized inverse matrix approach, pest control simulation

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Authors: Jolly Shah, S.S.Rattan, B.C.Nakra

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Automatic control of the robotic manipulator involves study of kinematics and dynamics as a major issue. This paper involves the forward and inverse kinematics of 2-DOF robotic manipulator with revolute joints. In this study the Denavit- Hartenberg (D-H) model is used to model robot links and joints. Also forward and inverse kinematics solution has been achieved using Artificial Neural Networks for 2-DOF robotic manipulator. It shows that by using artificial neural network the solution we get is faster, acceptable and has zero error.

Keywords: Artificial Neural Network, Forward Kinematics, Inverse Kinematics, Robotic Manipulator

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Authors: V. K. Banga, Y. Singh, R. Kumar

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In this paper, we have proposed a low cost optimized solution for the movement of a three-arm manipulator using Genetic Algorithm (GA) and Analytical Hierarchy Process (AHP). A scheme is given for optimizing the movement of robotic arm with the help of Genetic Algorithm so that the minimum energy consumption criteria can be achieved. As compared to Direct Kinematics, Inverse Kinematics evolved two solutions out of which the best-fit solution is selected with the help of Genetic Algorithm and is kept in search space for future use. The Inverse Kinematics, Fitness Value evaluation and Binary Encoding like tasks are simulated and tested. Although, three factors viz. Movement, Friction and Least Settling Time (or Min. Vibration) are used for finding the Fitness Function / Fitness Values, however some more factors can also be considered.

Keywords: Inverse Kinematics, Genetic Algorithm (GA), Analytical Hierarchy Process (AHP), Fitness Value, Fitness Function.

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Authors: P. Joyce Beryl Princess, Y. Harold Robinson

Abstract:

Image Processing is a structure of Signal Processing for which the input is the image and the output is also an image or parameter of the image. Image Resolution has been frequently referred as an important aspect of an image. In Image Resolution Enhancement, images are being processed in order to obtain more enhanced resolution. To generate highly resoluted image for a low resoluted input image with high PSNR value. Stationary Wavelet Transform is used for Edge Detection and minimize the loss occurs during Downsampling. Inverse Discrete Wavelet Transform is to get highly resoluted image. Highly resoluted output is generated from the Low resolution input with high quality. Noisy input will generate output with low PSNR value. So Noisy resolution enhancement technique has been used for adaptive sub-band thresholding is used. Downsampling in each of the DWT subbands causes information loss in the respective subbands. SWT is employed to minimize this loss. Inverse Discrete wavelet transform (IDWT) is to convert the object which is downsampled using DWT into a highly resoluted object. Used Image denoising and resolution enhancement techniques will generate image with high PSNR value. Our Proposed method will improve Image Resolution and reached the optimized threshold.

Keywords: Image Processing, Inverse Discrete wavelet transform, PSNR.

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Authors: F. Caliskan

Abstract:

This paper presents a Neural Network (NN) identification of icing parameters in an A340 aircraft and a reconfiguration technique to keep the A/C performance close to the performance prior to icing. Five aircraft parameters are assumed to be considerably affected by icing. The off-line training for identifying the clear and iced dynamics is based on the Levenberg-Marquard Backpropagation algorithm. The icing parameters are located in the system matrix. The physical locations of the icing are assumed at the right and left wings. The reconfiguration is based on the technique known as the control mixer approach or pseudo inverse technique. This technique generates the new control input vector such that the A/C dynamics is not much affected by icing. In the simulations, the longitudinal and lateral dynamics of an Airbus A340 aircraft model are considered, and the stability derivatives affected by icing are identified. The simulation results show the successful NN identification of the icing parameters and the reconfigured flight dynamics having the similar performance before the icing. In other words, the destabilizing icing affect is compensated.

Keywords: Aircraft Icing, Stability Derivatives, Neural NetworkIdentification, Reconfiguration.

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Authors: Baki Koyuncu, Mehmet Güzel

Abstract:

The kinematics of manipulators is a central problem in the automatic control of robot manipulators. Theoretical background for the analysis of the 5 Dof Lynx-6 educational Robot Arm kinematics is presented in this paper. The kinematics problem is defined as the transformation from the Cartesian space to the joint space and vice versa. The Denavit-Harbenterg (D-H) model of representation is used to model robot links and joints in this study. Both forward and inverse kinematics solutions for this educational manipulator are presented, An effective method is suggested to decrease multiple solutions in inverse kinematics. A visual software package, named MSG, is also developed for testing Motional Characteristics of the Lynx-6 Robot arm. The kinematics solutions of the software package were found to be identical with the robot arm-s physical motional behaviors.

Keywords: Lynx 6, robot arm, forward kinematics, inverse kinematics, software, DH parameters, 5 DOF , SSC-32 , simulator.

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Authors: Anatoli Torokhti, Stanley Miklavcic

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Suppose KY and KX are large sets of observed and reference signals, respectively, each containing N signals. Is it possible to construct a filter F : KY → KX that requires a priori information only on few signals, p  N, from KX but performs better than the known filters based on a priori information on every reference signal from KX? It is shown that the positive answer is achievable under quite unrestrictive assumptions. The device behind the proposed method is based on a special extension of the piecewise linear interpolation technique to the case of random signal sets. The proposed technique provides a single filter to process any signal from the arbitrarily large signal set. The filter is determined in terms of pseudo-inverse matrices so that it always exists.

Keywords: Wiener filter, filtering of stochastic signals.

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Authors: H. Mohammadipanah, H. Zohoor

Abstract:

This paper presents kinematic and dynamic analysis of a novel 8-DOF hybrid robot manipulator. The hybrid robot manipulator under consideration consists of a parallel robot which is followed by a serial mechanism. The parallel mechanism has three translational DOF, and the serial mechanism has five DOF so that the overall degree of freedom is eight. The introduced manipulator has a wide workspace and a high capability to reduce the actuating energy. The inverse and forward kinematic solutions are described in closed form. The theoretical results are verified by a numerical example. Inverse dynamic analysis of the robot is presented by utilizing the Iterative Newton-Euler and Lagrange dynamic formulation methods. Finally, for performing a multi-step arc welding process, results have indicated that the introduced manipulator is highly capable of reducing the actuating energy.

Keywords: hybrid robot, closed form, inverse dynamic, actuating energy, arc welding

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Authors: J. Miao, C. W. Leung, C. S. Cheung, R. C. K. Leung

Abstract:

The present project was conducted with the circumferential-fuel-jets inverse diffusion flame (CIDF) burner burning liquefied petroleum gas (LPG) enriched with 50% of hydrogen fuel (H2). The range of stable operation of the CIDF burner in terms of Reynolds number (from laminar to turbulent flow regions), equivalence ratio and fuel jet velocity of LPG of the 50% H2-LPG mixed fuel was identified. Experiments were also carried out to investigate the flame structures of the LPG flame and LPG enriched H2 flame. Experimental results obtained from these two flames were compared to fully explore the influence of hydrogen addition on flame stability. Flame heights obtained by burning these two kinds of fuels at various equivalence ratios were compared and correlated with the Global Momentum Ratio (GMR).

Keywords: Flame stability, hydrogen enriched LPG, inverse diffusion flame.

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Authors: Han-Taw Chen, Chung-Hou Lai, Tzu-Hsiang Lin, Ge-Jang He

Abstract:

This study applies the inverse method and three- dimensional CFD commercial software in conjunction with the experimental temperature data to investigate the heat transfer and fluid flow characteristics of the plate-fin heat sink in a closed rectangular enclosure for various values of fin height. The inverse method with the finite difference method and the experimental temperature data is applied to determine the heat transfer coefficient. The k-ε turbulence model is used to obtain the heat transfer and fluid flow characteristics within the fins. To validate the accuracy of the results obtained, the comparison of the average heat transfer coefficient is made. The calculated temperature at selected measurement locations on the plate-fin is also compared with experimental data.

Keywords: Inverse method, FLUENT, k-ε model, Heat transfer characteristics, Plate-fin heat sink.

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Authors: M. S. Gadala, Khaled Ahmed, Elasadig Mahdi

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In this paper, we introduced a gradient-based inverse solver to obtain the missing boundary conditions based on the readings of internal thermocouples. The results show that the method is very sensitive to measurement errors, and becomes unstable when small time steps are used. The artificial neural networks are shown to be capable of capturing the whole thermal history on the run-out table, but are not very effective in restoring the detailed behavior of the boundary conditions. Also, they behave poorly in nonlinear cases and where the boundary condition profile is different. GA and PSO are more effective in finding a detailed representation of the time-varying boundary conditions, as well as in nonlinear cases. However, their convergence takes longer. A variation of the basic PSO, called CRPSO, showed the best performance among the three versions. Also, PSO proved to be effective in handling noisy data, especially when its performance parameters were tuned. An increase in the self-confidence parameter was also found to be effective, as it increased the global search capabilities of the algorithm. RPSO was the most effective variation in dealing with noise, closely followed by CRPSO. The latter variation is recommended for inverse heat conduction problems, as it combines the efficiency and effectiveness required by these problems.

Keywords: Inverse Analysis, Function Specification, Neural Net Works, Particle Swarm, Run Out Table.

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Authors: Vigen Arakelian

Abstract:

This paper deals with the study of devices for displacement of the mould base of blow-molding machines. The displacement of the mould in the studied case is carried out by a linear actuator, which ensures the descent of the mould base and by extension springs, which return the letter in the initial position. The aim of this paper is to study the inverse dynamics of the device for displacement of the mould base of blow-molding machines and to determine its optimum parameters for higher rate of production. In the other words, it is necessary to solve the inverse dynamic problem to find the equation of motion linking applied forces with displacements. This makes it possible to determine the stiffness coefficient of the spring to turn the mold base back to the initial position for a given time. The obtained results are illustrated by a numerical example. It is shown that applying a spring with stiffness returns the mould base of the blow molding machine into the initial position in 0.1 sec.

Keywords: Design, blow-molding machines, dynamics.

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Authors: D. I. De Souza, G. P. Azevedo, R. Rocha

Abstract:

In this paper we will develop a sequential life test approach applied to a modified low alloy-high strength steel part used in highway overpasses in Brazil.We will consider two possible underlying sampling distributions: the Normal and theInverse Weibull models. The minimum life will be considered equal to zero. We will use the two underlying models to analyze a fatigue life test situation, comparing the results obtained from both.Since a major chemical component of this low alloy-high strength steel part has been changed, there is little information available about the possible values that the parameters of the corresponding Normal and Inverse Weibull underlying sampling distributions could have. To estimate the shape and the scale parameters of these two sampling models we will use a maximum likelihood approach for censored failure data. We will also develop a truncation mechanism for the Inverse Weibull and Normal models. We will provide rules to truncate a sequential life testing situation making one of the two possible decisions at the moment of truncation; that is, accept or reject the null hypothesis H0. An example will develop the proposed truncated sequential life testing approach for the Inverse Weibull and Normal models.

Keywords: Sequential life testing, normal and inverse Weibull models, maximum likelihood approach, truncation mechanism.

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Authors: Andy Handouyahia, Tony Haddad, Frank Eaton

Abstract:

Recent quasi-experimental evaluation of the Canadian Active Labour Market Policies (ALMP) by Human Resources and Skills Development Canada (HRSDC) has provided an opportunity to examine alternative methods to estimating the incremental effects of Employment Benefits and Support Measures (EBSMs) on program participants. The focus of this paper is to assess the efficiency and robustness of inverse probability weighting (IPW) relative to kernel matching (KM) in the estimation of program effects. To accomplish this objective, the authors compare pairs of 1,080 estimates, along with their associated standard errors, to assess which type of estimate is generally more efficient and robust. In the interest of practicality, the authorsalso document the computationaltime it took to produce the IPW and KM estimates, respectively.

Keywords: Treatment effect, causal inference, observational studies, Propensity score based matching, Kernel Matching, Inverse Probability Weighting, Estimation methods for incremental effect.

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Authors: T. Hacib, M. R. Mekideche, N. Ferkha

Abstract:

This paper presents an approach which is based on the use of supervised feed forward neural network, namely multilayer perceptron (MLP) neural network and finite element method (FEM) to solve the inverse problem of parameters identification. The approach is used to identify unknown parameters of ferromagnetic materials. The methodology used in this study consists in the simulation of a large number of parameters in a material under test, using the finite element method (FEM). Both variations in relative magnetic permeability and electrical conductivity of the material under test are considered. Then, the obtained results are used to generate a set of vectors for the training of MLP neural network. Finally, the obtained neural network is used to evaluate a group of new materials, simulated by the FEM, but not belonging to the original dataset. Noisy data, added to the probe measurements is used to enhance the robustness of the method. The reached results demonstrate the efficiency of the proposed approach, and encourage future works on this subject.

Keywords: Inverse problem, MLP neural network, parametersidentification, FEM.

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Authors: Ionel D. Craiu, Mihai Nedelcu

Abstract:

Thin-walled cylinders are often used by the offshore industry as columns of floating installations. Based on observed strains, the inverse Finite Element Method (iFEM) may rebuild the deformation of structures. Structural Health Monitoring uses this approach extensively. However, the number of in-situ strain gauges is what determines how accurate it is, and for shell structures with complicated deformation, this number can easily become too high for practical use. Any thin-walled beam member's complicated deformation can be modeled by the Generalized Beam Theory (GBT) as a linear combination of pre-specified cross-section deformation modes. GBT uses bar finite elements as opposed to shell finite elements. This paper proposes an iFEM/GBT formulation for the shape sensing of thin-walled cylinders based on these benefits. This method significantly reduces the number of strain gauges compared to using the traditional inverse-shell finite elements. Using numerical simulations, dent damage detection is achieved by comparing the strain distributions of the undamaged and damaged members. The effect of noise on strain measurements is also investigated.

Keywords: Damage detection, generalized beam theory, inverse finite element method, shape sensing.

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Authors: M. P. Nanda Kumar, K. Dheeraj

Abstract:

The design of a feedback controller, so as to minimize a given performance criterion, for a general non-linear dynamical system is difficult; if not impossible. But for a large class of non-linear dynamical systems, the open loop control that minimizes a performance criterion can be obtained using calculus of variations and Pontryagin’s minimum principle. In this paper, the open loop optimal trajectories, that minimizes a given performance measure, is used to train the neural network whose inputs are state variables of non-linear dynamical systems and the open loop optimal control as the desired output. This trained neural network is used as the feedback controller. In other words, attempts are made here to solve the “inverse optimal control problem” by using the state and control trajectories that are optimal in an open loop sense.

Keywords: Inverse Optimal Control, Radial basis function neural network, Controller Design.

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Authors: Ioannis N. Koukoulis, Clio G. Vossou, Christopher G. Provatidis

Abstract:

The aim of the current work is to present a comparison among three popular optimization methods in the inverse elastostatics problem (IESP) of flaw detection within a solid. In more details, the performance of a simulated annealing, a Hooke & Jeeves and a sequential quadratic programming algorithm was studied in the test case of one circular flaw in a plate solved by both the boundary element (BEM) and the finite element method (FEM). The proposed optimization methods use a cost function that utilizes the displacements of the static response. The methods were ranked according to the required number of iterations to converge and to their ability to locate the global optimum. Hence, a clear impression regarding the performance of the aforementioned algorithms in flaw identification problems was obtained. Furthermore, the coupling of BEM or FEM with these optimization methods was investigated in order to track differences in their performance.

Keywords: Elastostatic, inverse problem, optimization.

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Authors: Han-Taw Chen, Tzu-Hsiang Lin, Chung-Hou Lai

Abstract:

The present study applies the inverse method and three-dimensional CFD commercial software in conjunction with the experimental temperature data to investigate the heat transfer and fluid flow characteristics of the plate-fin heat sink in a rectangular closed enclosure. The inverse method with the finite difference method and the experimental temperature data is applied to determine the approximate heat transfer coefficient. Later, based on the obtained results, the zero-equation turbulence model is used to obtain the heat transfer and fluid flow characteristics between two fins. T0 validate the accuracy of the results obtained, the comparison of the heat transfer coefficient is made. The obtained temperature at selected measurement locations of the fin is also compared with experimental data. The effect of the height of the rectangular enclosure on the obtained results is discussed.

Keywords: Inverse method, FLUENT, Plate-fin heat sink, Heat transfer characteristics.

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Authors: Arsham Borumand Saeid

Abstract:

In this note the notion of interval-valued fuzzy BG-algebras (briefly, i-v fuzzy BG-algebras), the level and strong level BG-subalgebra is introduced. Then we state and prove some theorems which determine the relationship between these notions and BG-subalgebras. The images and inverse images of i-v fuzzy BG-subalgebras are defined, and how the homomorphic images and inverse images of i-v fuzzy BG-subalgebra becomes i-v fuzzy BG-algebras are studied.

Keywords: BG-algebra, fuzzy BG-subalgebra, interval-valued fuzzy set, interval-valued fuzzy BG-subalgebra.

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Authors: V.Pavlika

Abstract:

In this paper a numerical algorithm is described for solving the boundary value problem associated with axisymmetric, inviscid, incompressible, rotational (and irrotational) flow in order to obtain duct wall shapes from prescribed wall velocity distributions. The governing equations are formulated in terms of the stream function ψ (x,y)and the function φ (x,y)as independent variables where for irrotational flow φ (x,y)can be recognized as the velocity potential function, for rotational flow φ (x,y)ceases being the velocity potential function but does remain orthogonal to the stream lines. A numerical method based on the finite difference scheme on a uniform mesh is employed. The technique described is capable of tackling the so-called inverse problem where the velocity wall distributions are prescribed from which the duct wall shape is calculated, as well as the direct problem where the velocity distribution on the duct walls are calculated from prescribed duct geometries. The two different cases as outlined in this paper are in fact boundary value problems with Neumann and Dirichlet boundary conditions respectively. Even though both approaches are discussed, only numerical results for the case of the Dirichlet boundary conditions are given. A downstream condition is prescribed such that cylindrical flow, that is flow which is independent of the axial coordinate, exists.

Keywords: Inverse problem, irrotational incompressible flow, Boundary value problem.

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Authors: R. B. Ogunrinde

Abstract:

This paper presents the development, analysis and implementation of an inverse polynomial numerical method which is well suitable for solving initial value problems in first order ordinary differential equations with applications to sample problems. We also present some basic concepts and fundamental theories which are vital to the analysis of the scheme. We analyzed the consistency, convergence, and stability properties of the scheme. Numerical experiments were carried out and the results compared with the theoretical or exact solution and the algorithm was later coded using MATLAB programming language.

Keywords: Differential equations, Numerical, Initial value problem, Polynomials.

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