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This study introduces a new concept of decomposition methods for solving singular and nonlinear reaction-diffusion partial differential equations involving mixed derivative terms. The latest intercardinal finite difference structures are introduced for fast and accurate approximations of singular solutions. The exploration will demonstrate that the implicit schemes accomplished are numerically stable, convergent, efficient, and preservative for key physical parameters such as positivity and monotonicity. Dynamic orders of accuracy of the numerical algorithms will be estimated through generalized Milne’s devices. Simulation experiments of the intercardinal splitting methods will also be presented. Some open problems will be outlined for possible collaborations.

More information: https://sites.baylor.edu/qin_sheng/