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2-001-NumericalMethodsComparisons-TechniqueNarrative

Author(s): Swarn Singh

Sri Venkateswara College, University of Delhi

Keywords: Euler's method improved Euler's method RK3 methods RK4 methods order of accuracy absolute error CPU time

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Abstract

Resource Image This material teaches the basics of numerical methods for first order differential equations by following graphical and numerical approaches. We discuss the order of accuracy of the methods and compare their CPU times.

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Article Context

Resource Type
Differential Equation Type
Technique
Qualitative Analysis
Application Area
Course
Course Level
Lesson Length
Technology
Approach
Skills
Key Scientific Process Skills
Assessment Type
Vision and Change Core Competencies - Ability
Principles of How People Learn

Description

It is not always possible to solve a differential equation analytically.

When it is not possible to find analytic solutions for a differential equation, numerical methods are often used.

When an analytic solution of a differential equation is possible, but it is time-consuming, then the approximation obtained with a numerical solution could be appropriate.

To solve a given differential equation, we replace the derivatives by finite differences, based on the limit definition of the derivative.

The methods we offer provide algebraic equations for implementation on computers.

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Authors

Author(s): Swarn Singh

Sri Venkateswara College, University of Delhi

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