Implementation of DIMSIMs for stiff differential systems

• Published in: Applied numerical mathematics Vol. 42; no. 1; pp. 251 - 267
• Main Author: Jackiewicz, Z.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Amsterdam Elsevier B.V 01.08.2002; Elsevier
• Subjects: DIMSIMs; Exact sciences and technology; Local error estimation for stiff systems; Mathematical analysis; Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); Nordsieck representation; Numerical analysis. Scientific computation; Ordinary differential equations; Sciences and techniques of general use; Simplified Newton iterations; Nordsieck representation; DIMSIMs; Simplified Newton iterations; Local error estimation for stiff systems; Integration; Multistage; Numerical integration; Error estimation; Differential equation; Differential system; Eigenvalue; Iterative method; Iteration; Implementation; Equation system; Interpolation; Diagonally implicit multistage integration method; Eigenvalue problem; Newton method
• ISSN: 0168-9274; 1873-5460
• DOI: 10.1016/S0168-9274(01)00154-4

Some issues related to the implementation of diagonally implicit multistage integration methods for stiff differential systems are discussed. They include reliable estimation of the local discretization error, construction of continuous interpolants, solution of nonlinear systems of equations by simplified Newton iterations, choice of initial stepsize and order, and step and order changing strategy. Numerical results are presented which indicate that an experimental Matlab code based on type 2 methods of order one, two and three outperforms ode15s code from Matlab ODE suite on problems whose Jacobian has eigenvalues which are close to the imaginary axis.