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# Numerical Solution of ODEs Lecture Note

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## Description

Name of Notes : – Numerical Solution of ODEs Lecture Note

Introduction

Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as “numerical integration”, although this term can also refer to the computation of integrals.

Many differential equations cannot be solved using symbolic computation (“analysis”). For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation. An alternative method is to use techniques from calculus to obtain a series expansion of the solution.

Ordinary differential equations occur in many scientific disciplines, including physics, chemistry, biology, and economics.[1] In addition, some methods in numerical partial differential equations convert the partial differential equation into an ordinary differential equation, which must then be solved.

Modules / Lectures

• Introduction
• Single Step Methods
• Higher order Single Step Methods
• Systems of Equations and Equations of Order Greater Than One
• Consistency, Stability and Convergence of General Single – Step Methods
• Implicit Runge-Kutta Methods
• Multistep Methods
• Linear Multistep Methods
• Stiff-Initial Value Systems
• Finite Difference Methods for Boundary Value Problems

Product Name Numerical Solution of ODEs Lecture Note 2.76 MB Compressed Zip File PDF File Lecture Notes Mathematics Department College, Competition, Entrance, Exams, PSU, Semester, University Free Prof. M.K. Kadalbajoo IIT Kanpur Roop Chandra English

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