Numerical solution of the nonlinear Klein-Gordon equation using radial basis functions
By Mehdi Dehghan, Ali Shokri. 2009
358 citations recorded by the source corpus.
The nonlinear Klein-Gordon equation is used to model many nonlinear phenomena. In this paper, we propose a numerical scheme to solve the one-dimensional nonlinear Klein-Gordon equation with quadratic and cubic nonlinearity. Our scheme uses the collocation points and approximates the solution using Thin Plate Splines (TPS) radial basis functions (RBF). The implementation of the method is simple as finite difference methods. The results of numerical experiments are presented, and are compared with analytical solutions to confirm the good accuracy of the presented scheme.
Subfields: Mechanics of Materials, Modeling and Simulation, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/639c52052b9f99dc3801a84721b028c9c9ca5097
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Mechanics of Materials
- Natalya Shakhovska
- Kourosh Parand
- Wen Chen
- Saeid Abbasbandy
- Jamal Amani Rad
- Zakieh Avazzadeh
- Saeed Kazem
- Vahid Reza Hosseini
In Modeling and Simulation
- Wen Chen
- Natalya Shakhovska
- Kourosh Parand
- Saeid Abbasbandy
- Jamal Amani Rad
- Zakieh Avazzadeh
- Saeed Kazem
- Vahid Reza Hosseini
In Statistical and Nonlinear Physics
- Wen Chen
- Natalya Shakhovska
- Kourosh Parand
- Saeid Abbasbandy
- Jamal Amani Rad
- Zakieh Avazzadeh
- Saeed Kazem
- Vahid Reza Hosseini
Citations in the corpus
- A novel application of radial basis functions for solving a model of first-order integro-ordinary differential equation (2011, background): “As a result, many further interesting developments and applications have been reported [21–28].”
- Advances in Intelligent Systems and Computing (2016, methodology): “and those already available in literature [7, 12].”
- Numerical solution of fractional telegraph equation by using radial basis functions (2014, methodology): “The presented method is coupled of the radial basis functions and finite difference scheme as is handled in [1] [2] [5] [9] [10].”