A new Bernoulli matrix method for solving high-order linear and nonlinear Fredholm integro-differential equations with piecewise intervals

This article develops an efficient direct solver for solving numerically the high-order linear Fredholm integro-differential equations (FIDEs) with piecewise intervals under initial-boundary conditions. A Bernoulli matrix approach is implemented for solving linear and nonlinear FIDEs with piecewise...

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Bibliographic Details
Published in:Applied mathematics and computation 2012-10, Vol.219 (2), p.482-497
Main Authors: Bhrawy, A.H., Tohidi, E., Soleymani, F.
Format: Article
Language:English
Subjects:
Algebra
Boundary conditions
Computation
Intervals
Mathematical analysis
Mathematical models
Nonlinearity
Solvers
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Summary:This article develops an efficient direct solver for solving numerically the high-order linear Fredholm integro-differential equations (FIDEs) with piecewise intervals under initial-boundary conditions. A Bernoulli matrix approach is implemented for solving linear and nonlinear FIDEs with piecewise intervals under initial boundary conditions. The main characteristic behind this approach is that it reduces such problem to those of solving a system of algebraic equations. A small number of Bernoulli polynomials is needed to obtain a satisfactory result. Numerical results with comparisons are given to confirm the reliability of the proposed method for solving FIDEs with piecewise intervals.
ISSN:0096-3003
DOI:10.1016/j.amc.2012.06.020