Research on Locally Quadratic Convergence Algorithm for Linear Hyperbolic Equation 

Shuangcheng Jia, Tao Wang 

Alibaba Network Technology Co., Ltd., Beijing, 310013, China

Abstract: With vast calculating amount, the conventional convergence algorithm for linear hyperbolic prob-lem is quite complex, therefore, the quadratic convergence algorithm was proposed to resolve this problem. While the linear hyperbolic problem being proposed, the iterative sequences and algorithm complexity x be-ing introduced; the algorithm complexity being analyzed by using the local region and locally quadratic con-vergence; the problem of ellipse linear hyperbolic equation being taken as the example to analyze the prob-lems; and the numerical experiment being performed, the research on locally quadratic convergence algorithm for linear hyperbolic equation was completed. It can be proved by experiment that with less computation, the locally quadratic convergence algorithm is simpler than the conventional algorithm.

Keywords: Wide-neighborhood; Linear hyperbolic problem; Quadratic convergence