An exponentially convergent functional-discrete method for solving Sturm-Liouville problems with a potential including the Dirac delta-function

作者：Makarov V L; Rossokhata N O; Dragunova D V^*

来源：Journal of Computational and Applied Mathematics, 2013, 250: 39-57.

DOI：10.1016/j.cam.2013.02.015

• Sturm-Liouville problem
• Dirac delta-function
• Integrable potential
• Adomian polynomial
• Exponentially convergent algorithm
• Functional-discrete method

In this paper we present a functional-discrete method for solving Sturm-Liouville problems with a potential that includes a function from L-1 (0, 1) and the Dirac delta-function. For both the linear and the nonlinear case sufficient conditions for an exponential rate of convergence of the method are obtained. The question of a possible software implementation of the method is discussed in detail. The theoretical results are successfully confirmed by a numerical example.

• 出版日期2013-10-1