Numerical solution of nonlinear Klein-Gordon equation using the element-free kp-Ritz method
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal
Author(s)
Related Research Unit(s)
Detail(s)
| Original language | English |
|---|---|
| Pages (from-to) | 2917-2928 |
| Journal / Publication | Applied Mathematical Modelling |
| Volume | 39 |
| Issue number | 10-11 |
| Publication status | Published - 2015 |
Link(s)
Abstract
This paper presents a numerical analysis of the one-dimensional Klein-Gordon equation with quadratic and cubic nonlinearity, using the element-free reproducing kernel particle Ritz method (kp-Ritz method). Approximation of the wave displacement is expressed according to a set of meshfree kernel particle functions. Based on the established functional corresponding to the nonlinear Klein-Gordon equation, a system of nonlinear discrete equations can be obtained by applying the Ritz minimization procedure. The Newmark integration scheme combined with an iterative technique is applied to the resulting nonlinear system equations. Numerical examples are tested to validate the proposition that the presented numerical solutions are in good agreement with analytical results available in extant literature.
Research Area(s)
- Element-free kp-Ritz method, Meshless method, Newmark's integration scheme, Nonlinear Klein-Gordon equation
Citation Format(s)
Numerical solution of nonlinear Klein-Gordon equation using the element-free kp-Ritz method. / Guo, P. F.; Liew, K. M.; Zhu, P.
In: Applied Mathematical Modelling, Vol. 39, No. 10-11, 2015, p. 2917-2928.Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal
