Computer Methods in Applied Mechanics and Engineering
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Rosenbrock methods for partial differential equations and fractional orders of convergence
SIAM Journal on Numerical Analysis
A Second-Order Rosenbrock Method Applied to Photochemical Dispersion Problems
SIAM Journal on Scientific Computing
Solving unsymmetric sparse systems of linear equations with PARDISO
Future Generation Computer Systems - Special issue: Selected numerical algorithms
Computers & Mathematics with Applications
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The numerical treatment of quasi-static problems in solid mechanics incorporating constitutive equations of evolutionary type is pursued using the method of vertical lines. The spatial discretization is carried out by means of the finite element method. This yields large systems of differential-algebraic equations. In this article a new stiffly accurate Rosenbrock-type method of second order is proposed, which is applied to this challenging test case, and comparisons to existing Rosenbrock-type and diagonally-implicit Runge-Kutta methods are carried out.