Multivariable Linear Algebraic Discretization of Nonlinear Parabolic Equations for Computational Analysis

Abstract

Since the nonlinear parabolic equation has many variables, its calculation process is mostly an algebraic operation, which makes it difficult to express the discrete process concisely, which makes it difficult to effectively solve the two grid algorithm problems and the convergence problem of reaction diffusion. The extended mixed finite element method is a common method for solving reaction-diffusion equations. By introducing intermediate variables, the discretized algebraic equations have great nonlinearity. To address this issue, the paper proposes a multivariable linear algebraic discretization method for NPEs. First, the NPE is discretized, the algebraic form of the nonlinear equation is transformed into the vector form, and the rough set (RS) and information entropy (IE) are constructed to allocate the weights of different variable attributes. According to the given variable attribute weight, the multiple variables in the equation are discretized by linear algebra. It can effectively solve the two grid algorithm problems and the convergence problem of reaction diffusion and has good adaptability in this field.