Numerical solutions of systems of linear Fredholm integro-differential equations with Bessel polynomial bases (original) (raw)
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Mathematical and Computer Modelling, 2012
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In this paper a collocation method based on the Bessel-hybrid functions is used for approximation of the solution of linear Fredholm-Volterra integro-differential equations (FVIDEs) under mixed conditions. First, we explain the properties of Bessel-hybrid functions, which are combination of block-pulse functions and Bessel functions of first kind. The method is based upon Bessel-hybrid approximations, so that to obtain the operational matrixes and approximation of functions we use the transfer matrix from Bessel-hybrid functions to Taylor polynomials. The matrix equations correspond to a system of linear algebraic equations with the unknown Bessel-hybrid coefficients. Present results and comparisons demonstrate our estimate have good degree of accuracy. Mathematics Subject Classification (2010): 45A05, 45B05, 45D05, 65R20.
J. Sci. Kharazmi University, 2013
In this paper, a collocation method based on the Bessel polynomials is used for the solution of nonlinear Fredholm-Volterra-Hammerstein integro-differential equations (FVHIDEs) under mixed conditions. This method of estimating the solution, transforms the nonlinear (FVHIDEs) to matrix equations with the help of Bessel polynomials of the first kind and collocation points. The matrix equations correspond to a system of nonlinear algebraic equations with the unknown Bessel coefficients. Present results and comparisons demonstrate that our estimate has good degree of accuracy and this method is more valid and useful than other methods.
First international conference on combinatorics, cryptography and computation, 2016
In this article, approximate solutions of linear Volterra Integro-Differential equations system with variable coefficients types by means of the hybrid-Bessel method is considered. We use the transfer matrix from Bessel-hybrid functions to Taylor polynomials, to obtain the operational matrixes and approximation of functions. The matrix equations correspond to a system of linear algebraic equations with the unknown Bessel-hybrid coefficients. Some examples are given, showing its effectiveness and convenience.
International Journal of Informatics and Applied Mathematics
In this paper, a useful matrix approach for high-order linear Fredholm integro-differential equations with initial boundary conditions expressed as Lucas polynomials is proposed. Using a matrix equationwhich is equivalent to a set of linear algebraic equations the method transforms to integro-differential equation. When compared to other methods that have been proposed in the literature, the numerical results from the suggested technique reveal that it is effective and promising. And also, error estimation of the scheme was derived. These results were compared with the exact solutions and the other numerical methods to the tested problems.
TURKISH JOURNAL OF MATHEMATICS
In this article, a collocation method based on Pell-Lucas polynomials is studied to numerically solve higher order linear Fredholm-Volterra integro differential equations (FVIDE). The approximate solutions are assumed in form of the truncated Pell-Lucas polynomial series. By using Pell-Lucas polynomials and relations of their derivatives, the solution form and its derivatives are brought to matrix forms. By applying the collocation method based on equally spaced collocation points, the method reduces the problem to a system of linear algebraic equations. Solution of this system determines the coefficients of assumed solution. Error estimation is made and also a method with the help of the obtained approximate solution is developed that finds approximate solution with better results. Then, the applications are made on five examples to show that the method is successful. In addition, the results are supported by tables and graphs and the comparisons are made with other methods available in the literature. All calculations in this study have been made using codes written in Matlab.
Journal of Information and Computing Science, 2014
In this paper, a collocation method based on the Bessel polynomials are used for the solution of nonlinear Fredholm-Volterra-Hammerstein integral equations (FVHIEs). This method transforms the nonlinear (FVHIEs) in to matrix equations with the help of Bessel polynomials of the first kind and collocation points. The matrix equations corresponds to a system of nonlinear algebraic equations with the unknown Bessel coefficients. Present results demonstrate proposed method in comparison with other methods is more accurate, efficiency and reliability.
International Journal of Engineering Research and Technology (IJERT), 2014
https://www.ijert.org/numerical-solution-of-second-order-integro-differential-equationsides-with-different-four-polynomials-bases-functions https://www.ijert.org/research/numerical-solution-of-second-order-integro-differential-equationsides-with-different-four-polynomials-bases-functions-IJERTV3IS20283.pdf In this paper, a method based on the collocation methods with some bases functions are developed to find the numerical solution of Fredholm Integro-Differential Equations; four different polynomial bases functions used were: Legendary, Leguerre, Hermite and Fibonacci polynomial bases functions. The differential part appearing in the integro-differential equation is redefined and used to generate each of the polynomial bases functions. Some numerical results are given to demonstrate the superior performance of the various collocation methods, particularly, the table of error with the various value of N.
An operational matrix method for solving linear Fredholm--Volterra integro-differential equations
TURKISH JOURNAL OF MATHEMATICS, 2018
The aim of this paper is to propose an efficient method to compute approximate solutions of linear Fredholm-Volterra integro-differential equations (FVIDEs) using Taylor polynomials. More precisely, we present a method based on operational matrices of Taylor polynomials in order to solve linear FVIDEs. By using the operational matrices of integration and product for the Taylor polynomials, the problem for linear FVIDEs is transformed into a system of linear algebraic equations. The solution of the problem is obtained from this linear system after the incorporation of initial conditions. Numerical examples are presented to show the applicability and the efficiency of the method. Wherever possible, the results of our method are compared with those yielded by some other methods.