scholarly journals Error analysis of a Collocation method for numerically inverting a Laplace transform in case of real samples

2007 ◽  
Vol 210 (1-2) ◽  
pp. 149-158 ◽  
Author(s):  
S. Cuomo ◽  
L. D’Amore ◽  
A. Murli
Keyword(s):  
Error Analysis ◽  
Laplace Transform ◽  
Collocation Method ◽  
Real Samples

Numerical Solution of Nonlinear Volterra-Fredholm Integral Equations Using Haar Wavelet Collocation Method

2017 ◽  
Vol 18 ◽  
pp. 50-59 ◽  
Author(s):  
S.C. Shiralashetti ◽  
R.A. Mundewadi
Keyword(s):  
Integral Equation ◽  
Error Analysis ◽  
Numerical Solution ◽  
Integral Equations ◽  
Collocation Method ◽  
Haar Wavelet ◽  
Fredholm Integral Equations ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Wavelet Collocation Method

In this paper, we present a numerical solution of nonlinear Volterra-Fredholm integral equations using Haar wavelet collocation method. Properties of Haar wavelet and its operational matrices are utilized to convert the integral equation into a system of algebraic equations, solving these equations using MATLAB to compute the Haar coefficients. The numerical results are compared with exact and existing method through error analysis, which shows the efficiency of the technique.

Jacobi Collocation Approximation for Solving Multi-dimensional Volterra Integral Equations

2017 ◽  
Vol 18 (5) ◽  
pp. 411-425 ◽  
Author(s):  
Mohamed A. Abdelkawy ◽  
Ahmed Z. M. Amin ◽  
Ali H. Bhrawy ◽  
José A. Tenreiro Machado ◽  
António M. Lopes
Keyword(s):  
Error Analysis ◽  
Integral Equations ◽  
Collocation Method ◽  
Jacobi Polynomials ◽  
Volterra Integral Equations ◽  
The Novel ◽  
Two Dimensional ◽  
Numerical Examples ◽  
Novel Technique ◽  
Shifted Jacobi Polynomials

AbstractThis paper addresses the solution of one- and two-dimensional Volterra integral equations (VIEs) by means of the spectral collocation method. The novel technique takes advantage of the properties of shifted Jacobi polynomials and is applied for solving multi-dimensional VIEs. Several numerical examples demonstrate the efficiency of the method and an error analysis verifies the correctness and feasibility of the proposed method when solving VIE.

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