Solving (cyclic) tridiagonal systems
ACM SIGAPL APL Quote Quad
On the numerical integration of ordinary differential equations by symmetric composition methods
SIAM Journal on Scientific Computing
The book of GENESIS (2nd ed.): exploring realistic neural models with the GEneral NEural SImulation System
A Second-Order Rosenbrock Method Applied to Photochemical Dispersion Problems
SIAM Journal on Scientific Computing
Proceedings of the on Numerical methods for differential equations
An analysis of operator splitting techniques in the stiff case
Journal of Computational Physics
Journal of Computational Physics
Numerical Recipes in C: The Art of Scientific Computing
Numerical Recipes in C: The Art of Scientific Computing
The behaviour of the local error in splitting methods applied to stiff problems
Journal of Computational Physics
Adaptive moving mesh computations for reaction--diffusion systems
Journal of Computational and Applied Mathematics - Special issue: Selected papers from the 2nd international conference on advanced computational methods in engineering (ACOMEN2002) Liege University, Belgium, 27-31 May 2002
A Fourth-Order Time-Splitting Laguerre--Hermite Pseudospectral Method for Bose--Einstein Condensates
SIAM Journal on Scientific Computing
Hi-index | 31.45 |
Adaptive integration schemes for ODE systems typically function by adjusting the time step size so as to keep the truncation error below some desired value. For adaptive integration of PDE systems involving coupled kinetic reaction and diffusion operations, truncation error arises not only from the individual propagators but also from their method of coupling. A common second-order accurate method for coupling operators is Strang's method of operator splitting. We derive an expression for the truncation error resulting from Strang splitting reaction and diffusion operators for an arbitrary number of spatial dimensions, and demonstrate its use in adaptive time step algorithms. In addition, we present explanations of the second order implicit reaction and diffusion operators, and their individual error calculations used in our implementation of the scheme. Finally, using example simulations we discuss the use of this calculation for problems in systems biology.