MAT3041

Numerical solution of partial differential equations

Coordinator: Dr Paul Cally

4 points - Two 1-hour lectures and one 1-hour computer laboratory per week - First semester - Clayton - Prerequisites: MAT2030, MAT2040, MAT2072 - Prohibitions: ASP3111, ATM3141, MAA3011

Objectives On the completion of this subject, students will understand of the role of partial differential equations in the mathematical modelling of physical processes; distinguish between the three basic types of partial differential equations; understand the mathematical basis of approximating derivatives by their finite difference equivalents; appreciate the advantages and disadvantages of a range of methods for solving parabolic and hyperbolic partial differential equations; understand the role stability analysis based on the Fourier method; be able to apply systematic iterative methods for solving systems of finite-difference equations.

Synopsis Review of numerical solution of ordinary differential equations and finite-difference methods. Numerical techniques for parabolic and hyperbolic partial differential equations. Fourier stability analysis. Elliptic equations. Procedures for improving iterative processes.

Assessment Examination (2 hours): 70% - Assignments and class tests: 25% - Computer laboratory exercises: 5%

Recommended texts

Smith G D Numerical solution of partial differential equations 3rd edn, OUP, 1985

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