Analysis of stability and accuracy for forward time centered space approximation by using modified equation
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Date
2015
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Publisher
Science International
Abstract
In this paper we investigate the quantitative behavior of a wide range of numerical methods for solving linear partial
differential equations [PDE’s]. In order to study the properties of the numerical solutions, such as accuracy, consistency, and
stability, we use the method of modified equation, which is an effective approach.To determine the necessary and sufficient
conditions for computing the stability, we use a truncated version of modified equation which helps us in a better way to look
into the nature of dispersive as well as dissipative errors. The heat equation with Drichlet Boundary Conditions can serve as a
model for heat conduction, soil consolidation, ground water flow etc.Accuracy and Stability of Forward Time Centered Space
(FTCS) scheme is checked by using Modified Differential Equation [MDE].
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Keywords
Accuracy, Stability, Modified Equation, Dispersive error, Forward Time Center Space Scheme