|
|
 |
| |
|
|
|
A New Numerical Approach for the Solutions of Partial Differential Equations in Three-Dimensional Space |
|
|
|
PP: 1663-1672 |
|
|
|
doi:10.18576/amis/100504
|
|
|
|
Author(s) |
|
|
|
Brajesh Kumar Singh,
Carlo Bianca,
|
|
|
|
Abstract |
|
|
| This paper deals with the numerical computation of the solutions of nonlinear partial differential equations in threedimensional
space subjected to boundary and initial conditions. Specifically, the modified cubic B-spline differential quadrature method
is proposed where the cubic B-splines are employed as a set of basis functions in the differential quadrature method. The method
transforms the three-dimensional nonlinear partial differential equation into a system of ordinary differential equations which is solved
by considering an optimal five stage and fourth-order strong stability preserving Runge-Kutta scheme. The stability region of the
numerical method is investigated and the accuracy and efficiency of the method are shown by means of three test problems: the threedimensional
space telegraph equation, the Van der Pol nonlinear wave equation and the dissipative wave equation. The results show
that the numerical solution is in good agreement with the exact solution. Finally the comparison with the numerical solution obtained
with some numerical methods proposed in the pertinent literature is performed. |
|
|
|
|
|
|
|
