A novel numerical implementation for solving time fractional telegraph differential equations having multiple space and time delays via Delannoy polynomial

Abstract

 This paper is concerned with solving numerically the time fractional telegraph equations
having multiple space and time delays by proposing a novel matrix-collocation method
dependent on the Delannoy polynomial. This method enables easy and fast approximation
tool consisting of the matrix expansions of the functions using only the Delannoy
polynomial. Thus, the solutions are obtained directly from a unique matrix system. Also, the
residual error computation, which involves the same procedure as the method, provides the
improvement of the solutions. The method is evaluated under some valuable error tests in the
numerical applications. To do this, a unique computer module is devised. The present results
are compared with those of the existing methods in the literature, in order to oversee the
precision and efficiency of the method. One can express that the proposed method admits
very consistent approximation for the equations in question.

Keywords

• Delannoy polynomial
• matrix-collocation method
• multiple delays
• telegraph equation

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