Abstract
This paper concerns with the implementation of radial basis function pseudospectral (RBF-PS) method for solving Fisher’s equation. Pseudospectral methods are well known for being highly accurate but are limited in terms of geometric flexibility. Radial basis function (RBF) in combination with the pseudospectral method is capable to overcome this limitation. Using RBF, Fisher’s equation is approximated by transforming it into a system of ordinary differential equations (ODEs). An ODE solver is used to solve the resultant ODEs. In this approach, the optimal value of the shape parameter is discussed with the help of leave-one out cross validation strategy which plays an important role in the accuracy of the result. Several examples are given to demonstrate the accuracy and efficiency of the method. RBF-PS method is applied using different types of basis functions and a comparison is done based upon the numerical results. A two-dimensional problem that generalizes the Fisher’s equation is also solved numerically. The obtained numerical results and comparisons confirm that the use of RBF in pseudospectral mode is in good agreement with already known results in the literature.
Acknowledgments
The authors thank the reviewers for their useful comments and suggestions that improved the paper.
References
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Articles in the same Issue
- Frontmatter
- Original Research Articles
- Thermal Effect on Dynamics of Beam with Variable-Stiffness Nonlinear Energy Sink
- Nonlinear Dynamics Behavior of Tethered Submerged Buoy under Wave Loadings
- A Multistep Legendre Pseudo-Spectral Method for Nonlinear Volterra Integral Equations
- A Meshfree Numerical Technique Based on Radial Basis Function Pseudospectral Method for Fisher’s Equation
- Transient Simulation of Natural Gas Network by Hybrid Taguchi Binary Genetic Algorithm
- Numerical Analysis of TB32 Crash Tests for 4-cable Guardrail Barrier System Installed on the Horizontal Convex Curves of Road
- Nonlinear Vibration of Truncated Conical Shells: Donnell, Sanders and Nemeth Theories
- Singular Perturbed Vector Field (SPVF) Applied to Complex ODE System with Hidden Hierarchy Application to Turbocharger Engine Model
Articles in the same Issue
- Frontmatter
- Original Research Articles
- Thermal Effect on Dynamics of Beam with Variable-Stiffness Nonlinear Energy Sink
- Nonlinear Dynamics Behavior of Tethered Submerged Buoy under Wave Loadings
- A Multistep Legendre Pseudo-Spectral Method for Nonlinear Volterra Integral Equations
- A Meshfree Numerical Technique Based on Radial Basis Function Pseudospectral Method for Fisher’s Equation
- Transient Simulation of Natural Gas Network by Hybrid Taguchi Binary Genetic Algorithm
- Numerical Analysis of TB32 Crash Tests for 4-cable Guardrail Barrier System Installed on the Horizontal Convex Curves of Road
- Nonlinear Vibration of Truncated Conical Shells: Donnell, Sanders and Nemeth Theories
- Singular Perturbed Vector Field (SPVF) Applied to Complex ODE System with Hidden Hierarchy Application to Turbocharger Engine Model