Abstract
In this paper, we introduce a Hermite operational matrix collocation method for solving higher-order linear complex differential equations in rectangular or elliptic domains. We show that based on a linear algebra theorem, the use of different polynomials such as Hermite, Bessel and Taylor in polynomial collocation methods for solving differential equations leads to an equal solution, and the difference in the numerical results arises from the difference in the coefficient matrix of final linear systems of equations. Some numerical examples will also be given.
Highlights
Complex differential equations and their solutions play a major role in science and engineering
Since 1994, matrix polynomial collocation approaches such as Taylor and Bessel matrix collocation methods have been used by Sezer and colleagues [7,8,9,10,11] to solve the complex linear differential equations
The present work contains two main parts, in the first part, we use Hermite matrix collocation method to find the approximate solution of higher-order linear complex differential equations of the following form
Summary
Complex differential equations and their solutions play a major role in science and engineering. Since a few of these equations cannot be solved explicitly, it is often necessary to resort to approximation and numerical techniques. Since 1994, matrix polynomial collocation approaches such as Taylor and Bessel matrix collocation methods have been used by Sezer and colleagues [7,8,9,10,11] to solve the complex linear differential equations. The present work contains two main parts, in the first part, we use Hermite matrix collocation method to find the approximate solution of higher-order linear complex differential equations of the following form.
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