Approximate Solution of the Second Order Initial Value Problem by Using Epsilon Modified Block-Pulse Function
The present work approaches the problem of achieving the approximate solution of the second order initial value problems (IVPs) via its conversion into a Volterra integral equation of the second kind (VIE2). Therefore, we initially solve the IVPs using Runge–Kutta of the forth–order method (RK), and then convert it into VIE2, and apply the εmodified block–pulse functions (εMBPFs) and their operational matrix for solving VIE2, which can be transformed to a lower triangular system of algebric equations. Numerical examples show that the proposed scheme has a suitable degree of accuracy.
Numerical solution for boundary value problem of fractional order with approximate Integral and derivative
Approximating the solution of differential equations of fractional order is necessary because fractional differential equations have extensively been used in physics, chemistry as well as engineering fields. In this paper with central difference approximation and Newton Cots integration formula, we have found approximate solution for a class of boundary value problems of fractional order. Three...متن کامل
this paper presents an efficient modification of the variational iteration method for solvingboundary value problems using the chebyshev polynomials. the proposed method can be applied to linearand nonlinear models. the scheme is tested for some examples and the obtained results demonstrate thereliability and efficiency of the proposed method.متن کامل
NUMERICAL SOLUTIONS OF SECOND ORDER BOUNDARY VALUE PROBLEM BY USING HYPERBOLIC UNIFORM B-SPLINES OF ORDER 4
In this paper, using the hyperbolic uniform spline of order 4 we develop the classes of methods for the numerical solution of second order boundary value problems (2VBP) with Dirichlet, Neumann and Cauchy types boundary conditions. The second derivativeis approximated by the three-point central difference scheme. The approximate results, obtained by the proposed method, confirm theconvergence o...متن کامل
Generalized solution on Neumann problem of the fourth order ordinary differential equation in space $W^2_alpha(0,b)$ has been discussed, we obtain the condition on B.V.P when the solution is in classical form. Formulation of Quintic Spline Function has been derived and the consistency relations are given.Numerical method,based on Quintic spline approximation has been developed. Spline solution ...متن کامل
Theory of block-pulse functions in numerical solution of Fredholm integral equations of the second kind
Recently, the block-pulse functions (BPFs) are used in solving electromagnetic scattering problem, which are modeled as linear Fredholm integral equations (FIEs) of the second kind. But the theoretical aspect of this method has not fully investigated yet. In this article, in addition to presenting a new approach for solving FIE of the second kind, the theory of both methods is investigated as a...متن کامل
The multidimensional exponential Levy equations are used to describe many stochastic phenomena such as market fluctuations. Unfortunately in practice an exact solution does not exist for these equations. This motivates us to propose a numerical solution for n-dimensional exponential Levy equations by block pulse functions. We compute the jump integral of each block pulse function and present a ...متن کامل
دوره 9 شماره 4 (Fall)
صفحات 283- 295
تاریخ انتشار 2019-12-25
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