Search results for: generalized Pochhammer- Chree equation
1451 Some Solitary Wave Solutions of Generalized Pochhammer-Chree Equation via Exp-function Method
Authors: Kourosh Parand, Jamal Amani Rad
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In this paper, Exp-function method is used for some exact solitary solutions of the generalized Pochhammer-Chree equation. It has been shown that the Exp-function method, with the help of symbolic computation, provides a very effective and powerful mathematical tool for solving nonlinear partial differential equations. As a result, some exact solitary solutions are obtained. It is shown that the Exp-function method is direct, effective, succinct and can be used for many other nonlinear partial differential equations.
Keywords: Exp-function method, generalized Pochhammer- Chree equation, solitary wave solution, ODE's.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15821450 The BGMRES Method for Generalized Sylvester Matrix Equation AXB − X = C and Preconditioning
Authors: Azita Tajaddini, Ramleh Shamsi
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In this paper, we present the block generalized minimal residual (BGMRES) method in order to solve the generalized Sylvester matrix equation. However, this method may not be converged in some problems. We construct a polynomial preconditioner based on BGMRES which shows why polynomial preconditioner is superior to some block solvers. Finally, numerical experiments report the effectiveness of this method.Keywords: Linear matrix equation, Block GMRES, matrix Krylov subspace, polynomial preconditioner.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 8651449 Crank-Nicolson Difference Scheme for the Generalized Rosenau-Burgers Equation
Authors: Kelong Zheng, Jinsong Hu,
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In this paper, numerical solution for the generalized Rosenau-Burgers equation is considered and Crank-Nicolson finite difference scheme is proposed. Existence of the solutions for the difference scheme has been shown. Stability, convergence and priori error estimate of the scheme are proved. Numerical results demonstrate that the scheme is efficient and reliable.
Keywords: Generalized Rosenau-Burgers equation, difference scheme, stability, convergence.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18521448 Lagrangian Method for Solving Unsteady Gas Equation
Authors: Amir Taghavi, kourosh Parand, Hosein Fani
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In this paper we propose, a Lagrangian method to solve unsteady gas equation which is a nonlinear ordinary differential equation on semi-infnite interval. This approach is based on Modified generalized Laguerre functions. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also compare this work with some other numerical results. The findings show that the present solution is highly accurate.
Keywords: Unsteady gas equation, Generalized Laguerre functions, Lagrangian method, Nonlinear ODE.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15121447 Simulink Approach to Solve Fuzzy Differential Equation under Generalized Differentiability
Authors: N. Kumaresan , J. Kavikumar, Kuru Ratnavelu
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In this paper, solution of fuzzy differential equation under general differentiability is obtained by simulink. The simulink solution is equivalent or very close to the exact solution of the problem. Accuracy of the simulink solution to this problem is qualitatively better. An illustrative numerical example is presented for the proposed method.Keywords: Fuzzy differential equation, Generalized differentiability, H-difference and Simulink.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24281446 Solving of the Fourth Order Differential Equations with the Neumann Problem
Authors: Marziyeh Halimi, Roushanak Lotfikar, Simin Mansouri Borojeni
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In this paper we considered the Neumann problem for the fourth order differential equation. First we define the weighted Sobolev space 2 Wα and generalized solution for this equation. Then we consider the existence and uniqueness of the generalized solution, as well as give the description of the spectrum and of the domain of definition of the corresponding operator.Keywords: Neumann problem, weighted Sobolev spaces, generalized solution, spectrum of linear operators.2000 mathematic subject classification: 34A05, 34A30.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14211445 Transient Population Dynamics of Phase Singularities in 2D Beeler-Reuter Model
Authors: Hidetoshi Konno, Akio Suzuki
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The paper presented a transient population dynamics of phase singularities in 2D Beeler-Reuter model. Two stochastic modelings are examined: (i) the Master equation approach with the transition rate (i.e., λ(n, t) = λ(t)n and μ(n, t) = μ(t)n) and (ii) the nonlinear Langevin equation approach with a multiplicative noise. The exact general solution of the Master equation with arbitrary time-dependent transition rate is given. Then, the exact solution of the mean field equation for the nonlinear Langevin equation is also given. It is demonstrated that transient population dynamics is successfully identified by the generalized Logistic equation with fractional higher order nonlinear term. It is also demonstrated the necessity of introducing time-dependent transition rate in the master equation approach to incorporate the effect of nonlinearity.
Keywords: Transient population dynamics, Phase singularity, Birth-death process, Non-stationary Master equation, nonlinear Langevin equation, generalized Logistic equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15861444 Note to the Global GMRES for Solving the Matrix Equation AXB = F
Authors: Fatemeh Panjeh Ali Beik
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In the present work, we propose a new projection method for solving the matrix equation AXB = F. For implementing our new method, generalized forms of block Krylov subspace and global Arnoldi process are presented. The new method can be considered as an extended form of the well-known global generalized minimum residual (Gl-GMRES) method for solving multiple linear systems and it will be called as the extended Gl-GMRES (EGl- GMRES). Some new theoretical results have been established for proposed method by employing Schur complement. Finally, some numerical results are given to illustrate the efficiency of our new method.
Keywords: Matrix equation, Iterative method, linear systems, block Krylov subspace method, global generalized minimum residual (Gl-GMRES).
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18291443 Solution of Fuzzy Differential Equation under Generalized Differentiability by Genetic Programming
Authors: N. Kumaresan, J. Kavikumar, M. Kumudthaa, Kuru Ratnavelu
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In this paper, solution of fuzzy differential equation under general differentiability is obtained by genetic programming (GP). The obtained solution in this method is equivalent or very close to the exact solution of the problem. Accuracy of the solution to this problem is qualitatively better. An illustrative numerical example is presented for the proposed method.Keywords: Fuzzy differential equation, Generalized differentiability, Genetic programming and H-difference.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22361442 Solving Linear Matrix Equations by Matrix Decompositions
Authors: Yongxin Yuan, Kezheng Zuo
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In this paper, a system of linear matrix equations is considered. A new necessary and sufficient condition for the consistency of the equations is derived by means of the generalized singular-value decomposition, and the explicit representation of the general solution is provided.
Keywords: Matrix equation, Generalized inverse, Generalized singular-value decomposition.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20521441 A Boundary Backstepping Control Design for 2-D, 3-D and N-D Heat Equation
Authors: Aziz Sezgin
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We consider the problem of stabilization of an unstable heat equation in a 2-D, 3-D and generally n-D domain by deriving a generalized backstepping boundary control design methodology. To stabilize the systems, we design boundary backstepping controllers inspired by the 1-D unstable heat equation stabilization procedure. We assume that one side of the boundary is hinged and the other side is controlled for each direction of the domain. Thus, controllers act on two boundaries for 2-D domain, three boundaries for 3-D domain and ”n” boundaries for n-D domain. The main idea of the design is to derive ”n” controllers for each of the dimensions by using ”n” kernel functions. Thus, we obtain ”n” controllers for the ”n” dimensional case. We use a transformation to change the system into an exponentially stable ”n” dimensional heat equation. The transformation used in this paper is a generalized Volterra/Fredholm type with ”n” kernel functions for n-D domain instead of the one kernel function of 1-D design.Keywords: Backstepping, boundary control, 2-D, 3-D, n-D heat equation, distributed parameter systems.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16661440 Extending Global Full Orthogonalization method for Solving the Matrix Equation AXB=F
Authors: Fatemeh Panjeh Ali Beik
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In the present work, we propose a new method for solving the matrix equation AXB=F . The new method can be considered as a generalized form of the well-known global full orthogonalization method (Gl-FOM) for solving multiple linear systems. Hence, the method will be called extended Gl-FOM (EGl- FOM). For implementing EGl-FOM, generalized forms of block Krylov subspace and global Arnoldi process are presented. Finally, some numerical experiments are given to illustrate the efficiency of our new method.Keywords: Matrix equations, Iterative methods, Block Krylovsubspace methods.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19811439 Existence and Uniqueness of Positive Solution for Nonlinear Fractional Differential Equation with Integral Boundary Conditions
Authors: Chuanyun Gu
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By using fixed point theorems for a class of generalized concave and convex operators, the positive solution of nonlinear fractional differential equation with integral boundary conditions is studied, where n ≥ 3 is an integer, μ is a parameter and 0 ≤ μ < α. Its existence and uniqueness is proved, and an iterative scheme is constructed to approximate it. Finally, two examples are given to illustrate our results.Keywords: Fractional differential equation, positive solution, existence and uniqueness, fixed point theorem, generalized concave and convex operator, integral boundary conditions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11111438 On Method of Fundamental Solution for Nondestructive Testing
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14671437 Adomian Method for Second-order Fuzzy Differential Equation
Authors: Lei Wang, Sizong Guo
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In this paper, we study the numerical method for solving second-order fuzzy differential equations using Adomian method under strongly generalized differentiability. And, we present an example with initial condition having four different solutions to illustrate the efficiency of the proposed method under strongly generalized differentiability.
Keywords: Fuzzy-valued function, fuzzy initial value problem, strongly generalized differentiability, adomian decomposition method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 25291436 Exact Pfaffian and N-Soliton Solutions to a (3+1)-Dimensional Generalized Integrable Nonlinear Partial Differential Equations
Authors: Magdy G. Asaad
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The objective of this paper is to use the Pfaffian technique to construct different classes of exact Pfaffian solutions and N-soliton solutions to some of the generalized integrable nonlinear partial differential equations in (3+1) dimensions. In this paper, I will show that the Pfaffian solutions to the nonlinear PDEs are nothing but Pfaffian identities. Solitons are among the most beneficial solutions for science and technology, from ocean waves to transmission of information through optical fibers or energy transport along protein molecules. The existence of multi-solitons, especially three-soliton solutions, is essential for information technology: it makes possible undisturbed simultaneous propagation of many pulses in both directions.Keywords: Bilinear operator, G-BKP equation, Integrable nonlinear PDEs, Jimbo-Miwa equation, Ma-Fan equation, N-soliton solutions, Pfaffian solutions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20871435 Influences of Thermal Relaxation Times on Generalized Thermoelastic Longitudinal Waves in Circular Cylinder
Authors: Fatimah A. Alshaikh
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This paper is concerned with propagation of thermoelastic longitudinal vibrations of an infinite circular cylinder, in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters (Green and Lindsay theory). Three displacement potential functions are introduced to uncouple the equations of motion. The frequency equation, by using the traction free boundary conditions, is given in the form of a determinant involving Bessel functions. The roots of the frequency equation give the value of the characteristic circular frequency as function of the wave number. These roots, which correspond to various modes, are numerically computed and presented graphically for different values of the thermal relaxation times. It is found that the influences of the thermal relaxation times on the amplitudes of the elastic and thermal waves are remarkable. Also, it is shown in this study that the propagation of thermoelastic longitudinal vibrations based on the generalized thermoelasticity can differ significantly compared with the results under the classical formulation. A comparison of the results for the case with no thermal effects shows well agreement with some of the corresponding earlier results.
Keywords: Wave propagation, longitudinal vibrations, circular cylinder, generalized thermoelasticity, Thermal relaxation times.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21801434 Generalized Fuzzy Subalgebras and Fuzzy Ideals of BCI-Algebras with Operators
Authors: Yuli Hu, Shaoquan Sun
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The aim of this paper is to introduce the concepts of generalized fuzzy subalgebras, generalized fuzzy ideals and generalized fuzzy quotient algebras of BCI-algebras with operators, and to investigate their basic properties.Keywords: BCI-algebras with operators, generalized fuzzy subalgebras, generalized fuzzy ideals, generalized fuzzy quotient algebras.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 8091433 A Comparison of Marginal and Joint Generalized Quasi-likelihood Estimating Equations Based On the Com-Poisson GLM: Application to Car Breakdowns Data
Authors: N. Mamode Khan, V. Jowaheer
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In this paper, we apply and compare two generalized estimating equation approaches to the analysis of car breakdowns data in Mauritius. Number of breakdowns experienced by a machinery is a highly under-dispersed count random variable and its value can be attributed to the factors related to the mechanical input and output of that machinery. Analyzing such under-dispersed count observation as a function of the explanatory factors has been a challenging problem. In this paper, we aim at estimating the effects of various factors on the number of breakdowns experienced by a passenger car based on a study performed in Mauritius over a year. We remark that the number of passenger car breakdowns is highly under-dispersed. These data are therefore modelled and analyzed using Com-Poisson regression model. We use the two types of quasi-likelihood estimation approaches to estimate the parameters of the model: marginal and joint generalized quasi-likelihood estimating equation approaches. Under-dispersion parameter is estimated to be around 2.14 justifying the appropriateness of Com-Poisson distribution in modelling underdispersed count responses recorded in this study.
Keywords: Breakdowns, under-dispersion, com-poisson, generalized linear model, marginal quasi-likelihood estimation, joint quasi-likelihood estimation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14601432 A Novel System of Two Coupled Equations for the Longitudinal Components of the Electromagnetic Field in a Waveguide
Authors: Arti Vaish, Harish Parthasarathy
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In this paper, a novel wave equation for electromagnetic waves in a medium having anisotropic permittivity has been derived with the help of Maxwell-s curl equations. The x and y components of the Maxwell-s equations are written with the permittivity () being a 3 × 3 symmetric matrix. These equations are solved for Ex , Ey, Hx, Hy in terms of Ez, Hz, and the partial derivatives. The Z components of the Maxwell-s curl are then used to arrive to the generalized Helmholtz equations for Ez and Hz.Keywords: Electromagnetism, Maxwell's Equations, Anisotropic permittivity, Wave equation, Matrix Equation, Permittivity tensor.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16911431 An Iterative Algorithm to Compute the Generalized Inverse A(2) T,S Under the Restricted Inner Product
Authors: Xingping Sheng
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Let T and S be a subspace of Cn and Cm, respectively. Then for A ∈ Cm×n satisfied AT ⊕ S = Cm, the generalized inverse A(2) T,S is given by A(2) T,S = (PS⊥APT )†. In this paper, a finite formulae is presented to compute generalized inverse A(2) T,S under the concept of restricted inner product, which defined as < A,B >T,S=< PS⊥APT,B > for the A,B ∈ Cm×n. By this iterative method, when taken the initial matrix X0 = PTA∗PS⊥, the generalized inverse A(2) T,S can be obtained within at most mn iteration steps in absence of roundoff errors. Finally given numerical example is shown that the iterative formulae is quite efficient.Keywords: Generalized inverse A(2) T, S, Restricted inner product, Iterative method, Orthogonal projection.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12511430 The New Relative Efficiency Based on the Least Eigenvalue in Generalized Linear Model
Authors: Chao Yuan, Bao Guang Tian
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A new relative efficiency is defined as LSE and BLUE in the generalized linear model. The relative efficiency is based on the ratio of the least eigenvalues. In this paper, we discuss about its lower bound and the relationship between it and generalized relative coefficient. Finally, this paper proves that the new estimation is better under Stein function and special condition in some degree.Keywords: Generalized linear model, generalized relative coefficient, least eigenvalue, relative efficiency.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11841429 Flutter Analysis of Slender Beams with Variable Cross Sections Based on Integral Equation Formulation
Authors: Z. El Felsoufi, L. Azrar
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This paper studies a mathematical model based on the integral equations for dynamic analyzes numerical investigations of a non-uniform or multi-material composite beam. The beam is subjected to a sub-tangential follower force and elastic foundation. The boundary conditions are represented by generalized parameterized fixations by the linear and rotary springs. A mathematical formula based on Euler-Bernoulli beam theory is presented for beams with variable cross-sections. The non-uniform section introduces non-uniformity in the rigidity and inertia of beams and consequently, more complicated equilibrium who governs the equation. Using the boundary element method and radial basis functions, the equation of motion is reduced to an algebro-differential system related to internal and boundary unknowns. A generalized formula for the deflection, the slope, the moment and the shear force are presented. The free vibration of non-uniform loaded beams is formulated in a compact matrix form and all needed matrices are explicitly given. The dynamic stability analysis of slender beam is illustrated numerically based on the coalescence criterion. A realistic case related to an industrial chimney is investigated.
Keywords: Chimney, BEM and integral equation formulation, non uniform cross section, vibration and Flutter.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16151428 Generalized Chebyshev Collocation Method
Authors: Junghan Kim, Wonkyu Chung, Sunyoung Bu, Philsu Kim
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In this paper, we introduce a generalized Chebyshev collocation method (GCCM) based on the generalized Chebyshev polynomials for solving stiff systems. For employing a technique of the embedded Runge-Kutta method used in explicit schemes, the property of the generalized Chebyshev polynomials is used, in which the nodes for the higher degree polynomial are overlapped with those for the lower degree polynomial. The constructed algorithm controls both the error and the time step size simultaneously and further the errors at each integration step are embedded in the algorithm itself, which provides the efficiency of the computational cost. For the assessment of the effectiveness, numerical results obtained by the proposed method and the Radau IIA are presented and compared.
Keywords: Generalized Chebyshev Collocation method, Generalized Chebyshev Polynomial, Initial value problem.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 26261427 The Gerber-Shiu Functions of a Risk Model with Two Classes of Claims and Random Income
Authors: Shan Gao
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In this paper, we consider a risk model involving two independent classes of insurance risks and random premium income. We assume that the premium income process is a Poisson Process, and the claim number processes are independent Poisson and generalized Erlang(n) processes, respectively. Both of the Gerber- Shiu functions with zero initial surplus and the probability generating functions (p.g.f.) of the Gerber-Shiu functions are obtained.
Keywords: Poisson process, generalized Erlang risk process, Gerber-Shiu function, generating function, generalized Lundberg equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13061426 The Particle Swarm Optimization Against the Runge’s Phenomenon: Application to the Generalized Integral Quadrature Method
Authors: A. Zerarka, A. Soukeur, N. Khelil
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In the present work, we introduce the particle swarm optimization called (PSO in short) to avoid the Runge-s phenomenon occurring in many numerical problems. This new approach is tested with some numerical examples including the generalized integral quadrature method in order to solve the Volterra-s integral equations
Keywords: Integral equation, particle swarm optimization, Runge's phenomenon.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14091425 (T1, T2)*- Semi Star Generalized Locally Closed Sets
Authors: M. Sundararaman, K. Chandrasekhara Rao
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The aim of this paper is to continue the study of (T1, T2)-semi star generalized closed sets by introducing the concepts of (T1, T2)-semi star generalized locally closed sets and study their basic properties in bitopological spaces.
Keywords: (T1, T2)*-semi star generalized locally closed sets, T1T2-semi star generalized closed sets.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14631424 On the Integer Solutions of the Pell Equation x2 - dy2 = 2t
Authors: Ahmet Tekcan, Betül Gezer, Osman Bizim
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Let k ≥ 1 and t ≥ 0 be two integers and let d = k2 + k be a positive non-square integer. In this paper, we consider the integer solutions of Pell equation x2 - dy2 = 2t. Further we derive a recurrence relation on the solutions of this equation.
Keywords: Pell equation, Diophantine equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23741423 Cubic Trigonometric B-spline Approach to Numerical Solution of Wave Equation
Authors: Shazalina Mat Zin, Ahmad Abd. Majid, Ahmad Izani Md. Ismail, Muhammad Abbas
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The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature.
Keywords: Collocation method, Cubic trigonometric B-spline, Finite difference, Wave equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 25961422 New Application of EHTA for the Generalized(2+1)-Dimensional Nonlinear Evolution Equations
Authors: Mohammad Taghi Darvishi, Maliheh Najafi, Mohammad Najafi
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In this paper, the generalized (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff (shortly CBS) equations are investigated. We employ the Hirota-s bilinear method to obtain the bilinear form of CBS equations. Then by the idea of extended homoclinic test approach (shortly EHTA), some exact soliton solutions including breather type solutions are presented.
Keywords: EHTA, (2+1)-dimensional CBS equations, (2+1)-dimensional breaking solution equation, Hirota's bilinear form.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1481