This method is called the Newton - Raphson method or is more frequently referred to as Newton's Method . The iterative function associated with Newton's method is given by G ( x ) = x f ( x ) / f ' ( x ) . Differentiating with respect ...
A practical and concise guide to finite difference and finite element methods. Well-tested MATLAB® codes are available online.
Introduction to the Numerical Solution of Differential Equations
This book shows how to derive, test and analyze numerical methods for solving differential equations, including both ordinary and partial differential equations.
J. Baumgarte. “Stabilization of constraints and integrals of motion in dynamical systems”, Computer Methods in Applied Mechanics and ... J.C. Butcher. “Implicit Runge-Kutta processes”, Math. Comp. 18 (1964), pp. 50-64. J .C. Butcher.
This second edition of a highly successful graduate text presents a complete introduction to partial differential equations and numerical analysis.
Numerical Solution of Differential Equations
This book presents methods for the computational solution of differential equations, both ordinary and partial, time-dependent and steady-state.
An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics.
This is a valuable text for students, who will find the derivations of the numerical methods extremely helpful and the programs themselves easy to use.
This is the 2005 second edition of a highly successful and well-respected textbook on the numerical techniques used to solve partial differential equations arising from mathematical models in science, engineering and other fields.