Abstract
This study aimed at investigating a local radial basis function collocation method (LRBFCM) in the reproducing kernel Hilbert space. This method was, in fact, a meshless one which applied the local sub-clusters of domain nodes for the approximation of the arbitrary field. For time-dependent partial differential equations (PDEs), it would be changed to a system of ordinary differential equations (ODEs). Here, we intended to decrease the error through utilizing variable shape parameter (VSP) strategies. This method was an appropriate way to solve the two-dimensional nonlinear coupled Burgers’ equations comprised of Dirichlet and mixed boundary conditions. Numerical examples indicated that the variable shape parameter strategies were more efficient than constant ones for various values of the Reynolds number.
Highlights
Contrary to conventional numerical methods in solving the partial differential equations (PDEs), meshless methods [1], it is not essential to utilize meshes
Collocation methods are, meshless and easy to program. They allow some kinds of approaches to solve the PDEs
We have proposed some strategies to choose the variable shape parameter (VSP): strategy 1 :
Summary
Contrary to conventional numerical methods in solving the partial differential equations (PDEs), meshless methods [1], it is not essential to utilize meshes. Collocation methods are, meshless and easy to program They allow some kinds of approaches to solve the PDEs. Considering the translation of kernels as trial functions, meshless collocation in asymmetric and symmetric forms is described in [2,3,4]. Considering the translation of kernels as trial functions, meshless collocation in asymmetric and symmetric forms is described in [2,3,4] It is highly successful, since the arising linear systems are easy to produce, leading to such good accuracy with the beneficial range of computational expenses. Since the arising linear systems are easy to produce, leading to such good accuracy with the beneficial range of computational expenses It has been newly proven [5] that the symmetric collocation [2,3] utilizing kernel basis is optimal along all linear
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