Adaptive numerical methods for two point boundary value problems

Thesis/Dissertation · Sun Jan 01 04:00:00 EST 1984

OSTI ID:5489479

Huslak, N S

The author considers the numerical solution of systems of ordinary differential equations with two-point linear boundary conditions. Adaptive methods for these systems deal with local pathological behavior of solution vectors in specialized ways. He discusses the usage of variable order and variable mesh strategies, error estimation techniques, and other key elements in adaptive numerical methods. Two new adaptive algorithms for solving these systems are proposed, developed, and tested. The first algorithm employs interpolation techniques, transient mesh points, and a binary search technique to obtain the desired adaptive features. In the second algorithm, a high order modified Runge-Kutta method with many embedded lower order methods, and a mesh halving strategy afford computational efficiency and highly feasible adaptive features. Illustrative numerical results are given for each algorithm to demonstrate the viability of the approaches to adaptive algorithm design.

• Research Organization: State Univ. of New York, Stony Brook (USA)
• OSTI ID: 5489479
• Country of Publication: United States
• Language: English

Related Subjects

657000* -- Theoretical & Mathematical Physics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ACCURACY
ALGORITHMS
BOUNDARY CONDITIONS
BOUNDARY-VALUE PROBLEMS
DIFFERENTIAL EQUATIONS
EQUATIONS
INTERPOLATION
ITERATIVE METHODS
MATHEMATICAL LOGIC
MESH GENERATION
NUMERICAL SOLUTION
RUNGE-KUTTA METHOD