The direct method of lines for the numerical solutions of interface problem Original Research Article

In this paper, a direct method of lines is proposed for solving the interface problem on a polygonal domain numerically. A suitable transformation of coordinates is introduced, then the interface problem is reduced to a variational-differential problem on a semi-infinite strip in the new variables ρ and φ. Furthermore, the variational-differentional problem is discretized respect with variable φ, thus we obtain the semi-discrete approximation of the interface problem. Finally, the optimal error estimate of the semi-discrete approximation is given and the numerical examples show that the direct method of lines is feasible and very effective for solving the interface problem numerically.