2134/33621
Cormac P. Murphy
Cormac P.
Murphy
Numerical methods for solving ordinary and partial differential equations
Loughborough University
2018
untagged
Information and Computing Sciences not elsewhere classified
2018-06-29 13:25:44
Thesis
https://repository.lboro.ac.uk/articles/thesis/Numerical_methods_for_solving_ordinary_and_partial_differential_equations/9405998
The numerical solution of ordinary differential equations will be the
main topics discussed in the first half of this thesis. In Chapter 2 initial value problems are examined and the resulting differential equations are solved
by using extrapolation techniques. Computer trials of the algorithm are
completed by a special ordinary differential equation tester program and the
statistics of its performance are compared with other established methods.
In the following Chapter the relevant theory and properties, associated
with Chebyshev polynomials, is presented. Then boundary value problems are
solved by representing the ordinary differential equations as a Chebyshev
series. Finally, similar methods are developed for the solution of partial
differential equations.