A collocation method to solve higher order linear complex differential equations in rectangular domains

Abstract

In this article, a collocation method is developed to find an approximate solution of higher order linear complex differential equations with variable coefficients in rectangular domains. This method is essentially based on the matrix representations of the truncated Taylor series of the expressions in equation and their derivates, which consist of collocation points defined in the given domain. Some numerical examples with initial and boundary conditions are given to show the properties of the method. All results were computed using a program written in scientific WorkPlace v5.5 and Maple v12.

A collocation approach for solving linear complex differential equations in rectangular domains

“…For convenience, if the last m rows of Equation (18) are replaced, the new augmented matrix of the above system is as follows [12][13][14][15][19][20][21]: .…”

“…If max 10 k j D 10 k (k positive integer) is prescribed, then the truncation limit N is increased until the values E z j at each of the points z j becomes smaller than the prescribed 10 k , see [12][13][14][15][19][20][21][22]].…”

“…The results show the efficiency and accuracy of the present work. All of the numerical computations have been performed on a computer using a program written in MATLAB v7.6.0 (R2008a).which is a generalized case of the complex differential equations given in [5,6,[16][17][18][19][20], with the mixed conditions m 1 X kD0 J X jD0 h a rk f .k/ j i D r ; r D 0, 1, : : : , m 1.(2)…”

“…which is a generalized case of the complex differential equations given in [5,6,[16][17][18][19][20], with the mixed conditions m 1 X kD0 J X jD0 h a rk f .k/ j i D r ; r D 0, 1, : : : , m 1.…”

Numerical Solution for High-Order Linear Complex Differential Equations By Hermite Polynomials

“…Different type of differential equations have been solved with taylor (Sezer and Yalçınbaş, 2009), Bessel (Yüzbaşı et al, 2011), laguerre , hermite (Yüzbaşı et al, 2011), legendre (Tohidi, 2012;Düşünceli and Çelik, 2015) and Fibonacci polynomials (Düşünceli and Çelik, 2017). In this paper, the matrix operates between the Hermite polynomials and their derivatives, we utilized the Hermite method to solve linear complex differential equation.…”