Abstract
In this paper, cubic trigonometric spline is used to solve nonlinear Volterra integral equations of second kind. Examples are illustrated to show the presented method’s efficiency and convenience.
Highlights
An integral equation is defined as an equation in which the unknown function to be determined appear under the integral sign
Many initial and boundary value problems associated with ordinary differential equation (ODE) and partial differential equation (PDE) can be transformed into problems of solving some approximate integral equations
To develop numerical methods to approximate the solution of second kind Volterra integral equations
Summary
An integral equation is defined as an equation in which the unknown function to be determined appear under the integral sign. The solution of integral equation can be approximated by using the non-polynomial spline functions and the collection method [4].Combination of affixed point method and cubic B-spline functions was used [5] to solve the integral equation numerically. To develop numerical methods to approximate the solution of second kind Volterra integral equations. There is another method to solve these problems, which is called the Laplace transform series decomposition method (LTSDM), butthe cubic trigonometric spline method is the best method. 2.Trigonometric cubic spline method:-[7] In a simple way, we take [a,b] as interval, in order to improve the numerical method for approximation solution of the following kind: Previous studies provided more details on trigonometric spline [7, 8, 9, 10]. 2.Trigonometric cubic spline method:-[7] In a simple way, we take [a,b] as interval, in order to improve the numerical method for approximation solution of the following kind:
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