Numerical Methods for Differential Equations.
Abstract
During the past two years the investigators have been able to develop a computer code which, on the basis of some preliminary experiments, has turned out to be quite competitive with a well established code. The algorithmic development phase of the research has led to several useful results. An eighth order method, which has second, fourth and sixth order methods embedded in it has been developed. The method possesses some of the best features of implicit Runge-Kutta and Gap schemes. A multiderivative generalization of the above schemes has also been realized. A sparse factorization for quasi-Newton type methods has been obtained. Algorithms for solving combined systems of linear and non-linear algebraic equations and matrix splitting have also been developed. A new algorithm has been found for updating the sparse LDU factorization of the approximation to the Jacobian of the system of equations. This method is relatively more efficient than the currently available methods. A practical updating method has been obtained that is in the Broyden family of updates and is in most cases better than the BFGS method. Some effort was directed towards improvement in the stability properties of Boundary Value Runge Kutta methods.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 29, 1986
- Accession Number
- ADA177283
Entities
People
- Reginald P. Tewarson
Organizations
- Stony Brook University