# A Two-parameter Family of Two-level Higher Order Difference Methods for the Two-dimensional Heat Equation

@article{Khalil1975ATF, title={A Two-parameter Family of Two-level Higher Order Difference Methods for the Two-dimensional Heat Equation}, author={H. Khalil and J. H. Giese}, journal={Ima Journal of Applied Mathematics}, year={1975}, volume={16}, pages={193-205} }

#### 5 Citations

A review of current studies on complexity of algorithms for partial differential equations

- Mathematics, Computer Science
- ACM '76
- 1976

We review current work in analytic computational complexity of sequential algorithms for partial differential equations. Included are studies which analyze and compare classes of algorithms for… Expand

Computer generation of difference approximations

- Mathematics
- 1979

An algorithmic approach, based on the method of undetermined coefficients, for generating difference approximation to partial differential operators is presented here. The approach is based on… Expand

Multiparameter families of difference approximations for the first initial boundary value problem for the heat equation in an arbitrary region

- Mathematics
- 1978

SummaryA symbolic technique is developed to automatically generate consistent multiparameter families of difference approximations to the heat equation with Dirichlet boundary conditions in arbitrary… Expand

NUMERICAL COMPLEXITY OF TEN-POINT DIFFERENCE METHODS FOR THE TWO-DIMENSIONAL HEAT OPERATOR

- Mathematics
- 1978

A five-parameter family of two-level 10-point difference approximations to the two-dimensional heat operator is presented. The stability of the family is studied and a unified account of the familiar… Expand

Symbolic/numeric algorithms for partial differential equations

- Mathematics, Computer Science
- SYMSAC '76
- 1976

A two-phase procedure is described for automatically producing multiparameter families of difference approximations to the heat operator, using a truncated series expansion to form the appropriate difference operator. Expand