A parameter uniform B-spline collocation method for solving singularly perturbed turning point problem having twin boundary layers

作者：Kadalbajoo Mohan K; Gupta Vikas^*

来源：International Journal of Computer Mathematics, 2010, 87(14): 3218-3235.

DOI：10.1080/00207160902980492

• singular perturbation problem
• turning points
• B-spline collocation
• Shishkin mesh
• boundary layer
• uniform convergence

A numerical scheme is proposed to solve singularly perturbed two-point boundary value problems with a turning point exhibiting twin boundary layers. The scheme comprises B-spline collocation method on a non-uniform mesh of Shishkin type. Asymptotic bounds are established for the derivative of the analytical solution of a turning point problem. The present method is boundary layer resolving as well as second-order accurate in the maximum norm. A brief analysis has been carried out to prove the uniform convergence with respect to the singular perturbation parameter epsilon by decomposing the solution into smooth and singular components. Some relevant numerical examples are also illustrated to verify computationally the theoretical aspects.

• 出版日期2010