Differential transformation method for solving one-space-dimensional telegraph equation

Abstract

Abstract. In this research, the Differential Transformation Method (DTM) has been utilized to solve the hyperbolic Telegraph equation. This method can be used to obtain the exact solutions of this equation. In the end, some numerical tests are presented to demonstrate the effectiveness and efficiency of the proposed method.Mathematical subject classification: 35Lxx, 35Qxx.

Numerical solution for system of singular nonlinear Volterra integro-differential equations by Newton-Product method

“…In [8], system of weakly singular Volterra integral equations has been considered. Similar problems can be found in [16][17][18][19][20][21].…”

The Numerical Study of a Hybrid Method for Solving Telegraph Equation

“…Example 1. We will consider the following linear telegraph equation with initial and boundary conditions [18]:…”

“…Several numerical methods were developed for solving 1D telegraph equation, for example, reduced differential transform method, differential quadrature method, new unconditionally stable difference schemes, Chebyshev tau method, dual reciprocity boundary integral equation, cubic B-spline collocation method, modified B-spline differential quadrature method, semi-discretization method, unconditionally stable ADI method, Rothe-wavelet method, collocation method, He's variational iteration method, dual reciprocity boundary integral equation method, etc. [1,[9][10][11][12][13][14][15][16][17][18][19]. The preferred hybrid method is used for solving many types of differential equations.…”

Análise do Método Multi-Passos com Transformada Diferencial Generalizada na Modelagem Fracionária

“…DA TRANSFORMADA DIFERENCIAL: EXTENSÃO E GENERALIZAÇÃO O método da transformada diferencial (DTM) permite resolver uma grande variedade de equações diferenciais de ordem inteira [11,20,21]. A transformada diferencial converte cada função (derivável infinitas vezes) na sequência dos seus coeficientes de Taylor.…”