reproducing kernel technique for singularly perturbed initial-boundary value systems with exponential initial layers

In this paper, a technique is presented for especially perturbed linear and nonlinearsystems of second order initial-boundary value problems with exponential initial layers. thetechnique is a combination of the area decomposition technique and the reproducing kerneltechnique. a proper reproducing kernel is constructed for initial layer area problem. somenumerical examples are probed the accuracy of the present thechnique. results acquired by thetechnique indicate the technique is magnetic