None required for Post Grad Level
OverviewMost differential equations which arise from physical systems cannot be solved explicitly in closed form, and thus numerical solutions are an invaluable way to obtain information about the underlying physical system. The first half of the module is concerned with ordinary differential equations. Several different numerical methods are introduced and error growth is studied. Both initial value and boundary value problems are investigated. The second half of the module deals with the numerical solution of partial differential equations. The syllabus includes: initial value problems for ordinary differential equations; Taylor methods; Runge-Kutta methods; multistep methods; error bounds and stability; boundary value problems for ordinary differential equations; finite difference schemes; difference schemes for partial differential equations; iterative methods; stability analysis.
This module appears in:
48 hours of Lectures and Classes.
Method of assessment
90% Examination, 10% Coursework
Burden and Faires Numerical Analysis. (Thomson, Brooks/Cole, 2005) Selected chapters.
A first course in the numerical analysis of differential equations - A. Iserles
Numerical solution of partial differential equations - K. W. Morton, D. F. Mayers
The Intended Subject Specific Learning Outcomes. On successful completion of the module students will:
a. Have a reasonable ability to solve differential equations using numerical methods;
b. Have a reasonable knowledge of different methods which are available;
c. Be aware of the errors involved when using different methods.
The Intended Generic Learning Outcomes. On successful completion of the Module, students will:
a. Have developed a logical mathematical approach to solving problems and will be able to solve problems which arise in mathematics and require a numerical treatment.
b. Have improved their ability to work independently.
c. Have improved their key skills in written communication, numeracy and problem solving.