Abstract In this paper, we have studied a method based on exponential splines for numerical solution of singularly perturbed two parameter boundary value problems. The problem is solved Shishkin mesh by using splines. Numerical results are tabulated different values the perturbation parameters. From results, it found that approximates exact very well.

The work is devoted to the construction of asymptotic behavior solution a singularly perturbed system equations parabolic type, in case when limit equation has regular singularity as small parameter tends zero. asymptotics such problems contains boundary layer functions.

The aim of this study is to develop a regularization method for boundary value problems parabolic equation. A singularly perturbed problem on the semiaxis considered in case “simple” rational turning point. To prove asymptotic convergence series, maximum principle used.