Automatic selection of the initial step size for an ODE solver
Journal of Computational and Applied Mathematics
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Diagonally-implicit multi-stage integration methods
Applied Numerical Mathematics
Applied Numerical Mathematics
SIAM Journal on Scientific Computing
A nonlinear optimization approach to the construction of general linear methods of high order
Journal of Computational and Applied Mathematics
SIAM Journal on Numerical Analysis
Applied Numerical Mathematics
Exploiting structure in the construction of DIMSIMs
Journal of Computational and Applied Mathematics
Journal of Scientific Computing
Error propagation of general linear methods for ordinary differential equations
Journal of Complexity
Computers & Mathematics with Applications
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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.