On approximate solutions of the generalized Volterra integral equation

2021 ◽

Vol 41 (1) ◽

pp. 1-14

Author(s):

Asma Akter Akhia ◽

Goutam Saha

Keyword(s):

Integral Equation ◽

Galerkin Method ◽

Volterra Integral Equation ◽

Numerical Solutions ◽

Laguerre Polynomials ◽

Hermite Polynomials ◽

Approximate Solutions ◽

Linear Combinations ◽

Galerkin Approximations ◽

Error Estimations

In this research, we have introduced Galerkin method for finding approximate solutions of Fredholm Volterra Integral Equation (FVIE) of 2nd kind, and this method shows the result in respect of the linear combinations of basis polynomials. Here, BF (product of Bernstein and Fibonacci polynomials), CH (product of Chebyshev and Hermite polynomials), CL (product of Chebyshev and Laguerre polynomials), FL (product of Fibonacci and Laguerre polynomials) and LLE (product of Legendre and Laguerre polynomials) polynomials are established and considered as basis function in Galerkin method. Also, we have tried to observe the behavior of all these approximate solutions finding from Galerkin method for different problems and then a comparison is shown using some standard error estimations. In addition, we observe the error graphs of numerical solutions in Galerkin method for different problems of FVIE of second kind. GANITJ. Bangladesh Math. Soc.41.1 (2021) 1–14

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On the Stability of Numerical Methods for Nonlinear Volterra Integral Equations

Discrete Dynamics in Nature and Society ◽

10.1155/2010/862538 ◽

2010 ◽

Vol 2010 ◽

pp. 1-18 ◽

Cited By ~ 1

Author(s):

E. Messina ◽

Y. Muroya ◽

E. Russo ◽

A. Vecchio

Keyword(s):

Integral Equation ◽

Numerical Methods ◽

Numerical Solution ◽

Volterra Integral Equation ◽

Linear Part ◽

Approximate Solutions ◽

Constant Sign ◽

Quadrature Methods ◽

Decay Of Solutions ◽

The Stability

Here we investigate the behavior of the analytical and numerical solution of a nonlinear second kind Volterra integral equation where the linear part of the kernel has a constant sign and we provide conditions for the boundedness or decay of solutions and approximate solutions obtained by Volterra Runge-Kutta and Direct Quadrature methods.

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Approximate solutions of the random volterra integral equation

Lecture Notes in Mathematics - Random Integral Equations with Applications to Stochastic Systems ◽

10.1007/bfb0059963 ◽

1971 ◽

pp. 48-75

Author(s):

Chris P. Tsokos ◽

W. J. Padgett

Keyword(s):

Integral Equation ◽

Volterra Integral Equation ◽

Approximate Solutions

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APPROXIMATE SOLUTIONS OF NONLINEAR VOLTERRA INTEGRAL EQUATION SYSTEMS

International Journal of Modern Physics B ◽

10.1142/s0217979210055524 ◽

2010 ◽

Vol 24 (32) ◽

pp. 6235-6258 ◽

Cited By ~ 1

Author(s):

SALIH YALÇINBAŞ ◽

KÜBRA ERDEM

Keyword(s):

Integral Equation ◽

Integral Equations ◽

Volterra Integral Equation ◽

Approximate Solutions ◽

Algebraic Equations ◽

Nonlinear Volterra Integral Equation ◽

Solution Function ◽

Taylor Coefficients ◽

Linear Algebraic Equations ◽

New System

The purpose of this study is to implement a new approximate method for solving system of nonlinear Volterra integral equations. The technique is based on, first, differentiating both sides of integral equations n times and then substituting the Taylor series the unknown functions in the resulting equation and later, transforming to a matrix equation. By merging these results, a new system which corresponds to a system of linear algebraic equations is obtained. The solution of this system yields the Taylor coefficients of the solution function. Some numerical results are also given to illustrate the efficiency of the method.

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Theoretical Error Analysis of Solution for Two-Dimensional Stochastic Volterra Integral Equations by Haar Wavelet

International Journal of Applied and Computational Mathematics ◽

10.1007/s40819-019-0739-3 ◽

2019 ◽

Vol 5 (6) ◽

Author(s):

M. Fallahpour ◽

M. Khodabin ◽

K. Maleknejad

Keyword(s):

Integral Equation ◽

Error Analysis ◽

Integral Equations ◽

Volterra Integral Equation ◽

Stochastic Integral ◽

Approximate Solutions ◽

Haar Wavelet ◽

Two Dimensional ◽

Essential Requirement ◽

Stochastic Integral Equations

Abstract The finding an efficient way to the approximate solutions of the stochastic integral equations is an essential requirement. In this paper we discuss the convergence analysis of the two-dimensional Haar wavelet functions (2D-HWFs) method for solve 2D linear stochastic Volterra integral equation. The illustrative examples are included to demonstrate the validity and applicability of this numerical method.

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