On the direct numerical solution of partial differential equations with application of hypermatrices

global results on some nonlinear partial differential equations for direct and inverse problems

در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...

Application of the block backward differential formula for numerical solution of Volterra integro-differential equations

In this paper, we consider an implicit block backward differentiation formula (BBDF) for solving Volterra Integro-Differential Equations (VIDEs). The approach given in this paper leads to numerical methods for solving VIDEs which avoid the need for special starting procedures. Convergence order and linear stability properties of the methods are analyzed. Also, methods with extensive stability r...

Numerical Solution of Partial Differential Equations

Preface These lecture notes are intended to supplement a one-semester graduate-level engineering course at The George Washington University in numerical methods for the solution of partial differential equations. Both finite difference and finite element methods are included. The main prerequisite is a standard undergraduate calculus sequence including ordinary differential equations. In genera...

Numerical Solution of Partial Differential Equations

Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this book, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Contents Preface to the first edition page viii Preface to the second edition xi 1 Introduction 1 2 Parabolic equations in one space v...

Numerical Solution of Nonlinear Partial Differential Equations