The immersed interface method for two-dimensional heat-diffusion equations with singular own sources

This paper develops the immersed interface method (IIM) due to [R.J. LeVeque, Z. Li, The immersed interface method for elliptic equations with discontinuous coefficients and singular sources, SIAM J. Numer. Anal. 31 (1994) 1019–1044] for solving parabolic equations with singular own sources. New finite difference schemes are constructed to satisfy the discrete maximum principle. Convergence proof is provided. Numerical experiments show the efficiency of the proposed schemes.