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    A Novel Time Integration Method for Solving A Large System of Non-Linear Algebraic Equations

    Chein-Shan Liu1, Satya N. Atluri2

    CMES-Computer Modeling in Engineering & Sciences, Vol.31, No.2, pp. 71-84, 2008, DOI:10.3970/cmes.2008.031.071

    Abstract Iterative algorithms for solving a nonlinear system of algebraic equations of the type: Fi(xj) = 0, i,j = 1,…,n date back to the seminal work of Issac Newton. Nowadays a Newton-like algorithm is still the most popular one due to its easy numerical implementation. However, this type of algorithm is sensitive to the initial guess of the solution and is expensive in the computations of the Jacobian matrix ∂ Fi/ ∂ xj and its inverse at each iterative step. In a time-integration of a system of nonlinear Ordinary Differential Equations (ODEs) of the type Bijxj + Fi = 0 where… More >

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