Investigation of the Numerical Methods of Finite Differences and Weighted Residuals for Solution of the Heat Equation.
Abstract
The method of weighted residuals applied on the whole domain for steady state and transient heat generation problems was compared to finite difference methods. The comparison consisted of the maximum absolute error from the exact solution and computer time required for solution. One steady state and one transient heat generation problem were solved by collocation and Galerkin weighted residual methods and finite differences. The least squares weighted residual method was also used for the steady state problem. Both problems were one-dimensional and had Dirichlet boundary conditions. Integrals for weighted residual methods were evaluated analytically to produce recursion relations. The transient problem was solved by the reduction to ordinary differential equations method for weighted residuals. The Galerkin method was fastest to a given accuracy for both problems evaluated. The accuracy of Galerkin and other weighted residual methods was greater than finite differences after a point at low solution accuracy. This crossover point was typically two to three digits of accuracy. The polynomial trial functions used for weighted residual solutions exhibited a numerical instability for solutions of 10 terms and over increasing the maximum absolute error. Orthogonal collocation and weighted residuals on finite elements were recommended as alternate methods. (Auhtor)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1982
- Accession Number
- ADA100815
Entities
People
- Robert Earl Naegeli
Organizations
- Air Force Institute of Technology