Unconditionally stable explicit schemes for non-linear diffusion wave routing

This paper introduces a methodology for developing unconditionally stable higher order explicit schemes for the solution of one dimensional non-linear diffusion equation. Based on the proposed methodology two new higher order schemes namely second order nodal and second order cell centered are developed. Unconditional stability is established using Von Neumann analysis. Results of the proposed schemes are compared with several popular schemes and analytical solutions. The proposed schemes are found to be superior to available schemes.