Nonlinear Algebraic Equations Solved by an Optimal Splitting-Linearizing Iterative Method.

Chein-Shan Liu; El-Zahar, Essam R.; Yung-Wei Chen

How to accelerate the convergence speed and avoid computing the inversion of a Jacobian matrix is important in the solution of nonlinear algebraic equations (NAEs). This paper develops an approach with a splitting-linearizing technique based on the nonlinear term to reduce the effect of the nonlinear terms. We decompose the nonlinear terms in the NAEs through a splitting parameter and then linearize the NAEs around the values at the previous step to a linear system. Through the maximal orthogonal projection concept, to minimize a merit function within a selected interval of splitting parameters, the optimal parameters can be quickly determined. In each step, a linear system is solved by the Gaussian elimination method, and the whole iteration procedure is convergent very fast. Several numerical tests show the high performance of the optimal split-linearization iterative method (OSLIM).

ALGEBRAIC equations; GAUSSIAN elimination; MATRIX inversion; ORTHOGRAPHIC projection; NONLINEAR equations; LINEAR systems; JACOBIAN matrices

Computer Modeling in Engineering & Sciences (CMES), 2023, Vol 135, Issue 2, p1111

1526-1492

Academic Journal

10.32604/cmes.2022.021655