A uniform numerical method for semilinear reaction-diffusion problems with a boundary turning point

作者：Vulanovic Relja; Teofanov Ljiljana^*

来源：Numerical Algorithms, 2010, 54(4): 431-444.

DOI：10.1007/s11075-009-9344-6

• One-dimensional reaction-diffusion problem
• Semilinear boundary-value problem
• Boundary turning point
• Singular perturbation
• Finite-difference method
• Layer-adapted mesh

Motivated by problems arising in semiconductor-device modeling, this paper is concerned with a singularly perturbed semilinear reaction-diffusion problem with a boundary turning point. It is proved that the problem has a unique solution with two boundary layers. Based on the estimates of the derivatives of the solution, a numerical method is proposed which uses the classical finite-difference discretization on a Bakhvalov-type mesh. Second-order accuracy, uniform with respect to the perturbation parameter, is proved in the maximum norm. Numerical results are presented in support of the theoretical ones.

• 出版日期2010-8