Improved Preconditioned Descent Algorithms For P-Laplacian

The p-Laplacian equation is one of the typical examples of degenerate non-linear systems, which widely occurs in the study of physics. Then, it is very important to research its numerical solution.This paper mainly includes the following contents.The first chapter introduces the research backgroud and current status of the pLaplacian equation, and some preliminary knowledge.The second chapter compares the effciency of precondioned steepest descent method and FR-PRP conjugate gradient methods through numerical example. Finding that FR-PRP conjugate gradient methods has higher effciency when the value of p is big. However, precondioned steepest descent method performs better when the value of p is near 1.1. Also, the choice of parameter ? is studied in its influence on numerical results, through many numerical experiments finding that the algorithms have the best effciency when the parameter ? ∈(10-5～ 10-3).Finally, adaptive selection fixed step length of precondioned steepest descent method is proposed, and numerical experiments demonstrate the feasibility of the algorithm.