A meshless method for numerical solution of the one-dimensional wave equation with an integral condition using radial basis functions

作者：Dehghan Mehdi^*; Shokri Ali

来源：Numerical Algorithms, 2009, 52(3): 461-477.

DOI：10.1007/s11075-009-9293-0

• Hyperbolic partial differential equation
• Nonlocal boundary condition
• Collocation
• Radial basis RBF)
• Thin plate splines (TPS)
• Multiquadrics (MQ)
• Inverse multiquadrics (IMQ)
• Gaussian (GA)
• Compactly supported RBFs
• Shape parameter

The hyperbolic partial differential equation with an integral condition arises in many physical phenomena. In this paper, we propose a numerical scheme to solve the one-dimensional hyperbolic equation that combines classical and integral boundary conditions using collocation points and approximating the solution using radial basis functions (RBFs). The results of numerical experiments are presented, and are compared with analytical solution and finite difference method to confirm the validity and applicability of the presented scheme.

• 出版日期2009-11