التحليل العددي للمعادلات التفاضلية الجزئية

Abstract

A form of numerical methods first found broad application in the solution of differential equations Von Neumann in the early Fifties in solving certain types of partial differential equations (PDEs). Numerical approaches for nonlinear PDEs can be primarily be affected by three different mechanisms: explicit computations, earlier PDE advancements, and prior numerology. Math models and the abstracted tools of the modern mathematics. More than 80% of the PDE theory was generated in response to physical-science models that were then applied to problems in other disciplines. classical examples of nonlinear partial differential equations, include the Schrödinger equation, the Navier–Stokes equation, and the Laplace equation (PDEs).Following the evolution of numerical approaches, we witness a comparable development. Within the past two decades, a substantial part of the theoretical physicists' theories of theorems have included nonlinear PDEs, which stem from social and biological science ideas. Because of its lacking in qualities that are present in Newtonian, Maxwellian, and Schrödingerian theories, this theory has low mathematical certainty.