Abstract
In this paper we may use piece wise constant functions for the special type of system of second kind integro differential equation of the first order. The main problem is reduced to linear system of algebraic equations. Some numerical examples are dedicated for showing efficiency and validity of the method.
Highlights
Many different basis functions are used for approximating the solution of integro differential equations like Haar wavelets, lagrange functions, Taylor polynomials, Chebyshev polynomials, sine-cosine wavelets, Tau method, Adomian decomposition method, hybrid Legendre and Block Pulse functions and so on [1-8]
For showing validity and efficiency, the method is applied for test problem with two different values of the parameter k which states approximations may be more accurate using larger k
The benefit of the method is simplicity for execution and using sparse matrices which make the method cheap as computational costs
Summary
Many different basis functions are used for approximating the solution of integro differential equations like Haar wavelets, lagrange functions, Taylor polynomials, Chebyshev polynomials, sine-cosine wavelets, Tau method, Adomian decomposition method, hybrid Legendre and Block Pulse functions and so on [1-8]. We use Block Pulse functions (BPfs) for solving system of Volterra integro differential equation of the form. Since the BPfs is not continuous so the derivatives don’t exist at these points of discontinuity we can’t apply the BPfs in a direct manner to solve differential equations. We may expand y1′(x), y2′ (x), , ym′ (x) into the BPfs series and y1(x), y2(x),...,ym(x) will be obtain through integration:. The k-square matrix P is called the operational matrix of integration of the transform and is defined as follows: Pk×k.
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