Abstract
The main aim presented in this article is to provide an efficient transferred Legendre pseudospectral method for solving pantograph delay differential equations. At the first step, we transform the problem into a continuous-time optimization problem and then utilize a transferred Legendre pseudospectral method to discretize the problem. By solving this discrete problem, we can attain the pointwise and continuous estimated solutions for the major pantograph delay differential equation. The convergence of method has been considered. Also, numerical experiments are described to show the performance and precision of the presented technique. Moreover, the obtained results are compared with those from other techniques.
Highlights
Many dynamical problems, in various sciences such as economics, medicine, biology, robotics, physics, control systems and other industrial applications, include a system of differential equations with initial or boundary conditions
The main reason for using spectral and pseudospectral methods is the exponential convergence rate of these methods in approximating analytical and smooth functions [7, 33, 35]. These methods usually deal with two steps: selecting a polynomial space to approximate the solution of problem and transferring the problem into the polynomial space
We propose a transferred Legendre pseudospectral method to solve a class of pantograph delay differential equations (PDDEs)
Summary
In various sciences such as economics, medicine, biology, robotics, physics, control systems and other industrial applications, include a system of differential equations with initial or boundary conditions. Xu and Huang [13, 42] found the discontinuous and continuous Galerkin solutions for the PDDEs. In [6], the trapezoidal rule discretization was investigated for numerical solution of the PDEs. In [8, 19], rational functions were applied to approximate a generalized pantograph equation on a semiinfinite interval. The main reason for using spectral and pseudospectral methods is the exponential convergence rate of these methods in approximating analytical and smooth functions [7, 33, 35] These methods usually deal with two steps: selecting a polynomial space to approximate the solution of problem and transferring the problem (or differential equation) into the polynomial space. J=0 is a continuous estimate solution for the CTO problem (2) (or the major equation (1))
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