An efficient multi-derivative numerical method for chemical boundary value problems

The singular and singularly perturbed boundary value problems (SBVPs and SPBVPs) arise in the modeling of various chemical processes such as the isothermal gas sphere, electroactive polymer film, thermal explosion, and chemical reactor theory. Efficient numerical methods are desirable for solving such problems with a wide scope of influence. Here we derive the implicit-explicit local differential transform method (IELDTM) based on the Taylor series to solve chemical SBVPs and SPBVPs. The differential equations are directly utilized to determine the local Taylor coefficients and the entire system of algebraic equations is assembled using explicit/implicit continuity relations regarding the direction parameter. The IELDTM has an effective h-p refinement property and increasing the order of the method does not affect the degrees of freedom. We have validated the theoretical convergence results of the IELDTM with various numerical experiments and provided detailed discussions. It has been proven that the IELDTM yields more accurate solutions with fewer CPU times than various recent numerical methods for solving chemical BVPs.