Properties of analytic solution and numerical solution of multi-pantograph equation

A taylor collocation method for solving high-order linear pantograph equations with linear functional argument

“…Here, µ 1 (t) = −e −0.5t sin(0.5t), µ 2 (t) = −2e −0.75t cos(0.5t) sin(0.25t). It can be seen that the exact solution of this problem is y(t) = e −t cos(t) [1]. We give numerical analysis for various N values in Table IV.…”

“…We make a comparison between Adomian series [1] and present collocation methods, and also we give accuracy of the solution in Table V. It can be seen that the exact solution of this problem is y(t) = e −t .…”

“…which is a generalized of the pantograph equations given in [1][2][3]17], with the initial conditions …”

“…In recent years, pantograph equations have been studied by many authors, who have investigated both their analytical and numerical aspects [1][2][3][4][5]. Pantograph equations are characterized by the presence of a linear functional argument and play an important role in explaining many different phenomena.…”

Two Numerical Methods to Solve the Second Order Multi-pantograph Equation with Boundary Conditions

“…The following second order delay differential [6,7,8] by Sezer et al and θ-method [4] by Liu and Li. Saadatmandi and Dehghan applied the variational iteration method in [5] and Yu in [15] as well.…”