Numerical Solutions of Initial Value Problems
NAVAL UNDERWATER SYSTEMS CENTER NEW LONDON CT
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A family of nonlinear multistep NLMS numerical methods has been developed that is particularly effective for solving stiff ordinary differential equations. These methods offer the advantages of avoiding small step sizes and being A-stable in the Dahlquist sense. These advantages over existing conventional and stiff methods have been demonstrated by the present author with a number of test cases. These same methods can also be used to solve nonasymptotically stable differential equations since they are a generalization of Linear Multistep LMS methods. This report presents a detailed formulation of NLMS methods and discusses a FORTRAN V computer package specifically developed to implement NLMS methods. The package, also available in ANSI FORTRAN, is presently operational on Univac 1108, IBM 360370, and CDC 6600 computers. Several desirable features are included in the computer program, namely, a fixed or variable step size, sefl-start, a selection of characteristic polynomial coefficients, predict-and-correct m times, and the inclusion of LMS methods.
- Theoretical Mathematics