A Numerical Approach with Residual Error Estimation for Eolution of High-order Linear Differential-difference Equations by Using Gegenbauer Polynomials
The main aim of this
study is to apply the Gegenbauer polynomials for the solution of high-order
linear differential difference equations with functional arguments under
initial-boundary conditions.The technique we have used is essentially based on
the truncated Gegenbauer series and its matrix representations along with
collocation points. Also, by using the Mean-Value Theorem and residual
function, an efficient error estimation technique is proposed and some
illustrative examples are presented to demonstrate the validity and
applicability of the method.
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- M. T. Rashed, Numerical solution of functional differential,integral and integro- differential equations, Appl.Math.Comput.156 (2004) 485-492.