Transcription of Finite-Di erence Approximations to the Heat Equation
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Finite-Di erence Approximations to the Heat Equation
finite -Difference Approximations to the heat Equation Gerald W. Recktenwald . March 6, 2011. Abstract This article provides a practical overview of numerical solutions to the heat Equation using the finite difference method. The forward time, centered space (FTCS), the backward time, centered space (BTCS), and Crank-Nicolson schemes are developed, and applied to a simple problem involving the one-dimensional heat Equation . Complete, working Mat- lab codes for each scheme are presented. The results of running the codes on finer (one-dimensional) meshes, and with smaller time steps is demonstrated. These sample calculations show that the schemes real- ize theoretical predictions of how their truncation errors depend on mesh spacing and time step.
Finite-Di erence Approximations to the Heat Equation Gerald W. Recktenwald March 6, 2011 Abstract This article provides a practical overview of numerical solutions to
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