How to parallelise numerical integration (ode45)?

I would like to apply ode45 to a matrix with 2 lines and 10000 rows. In the matrix each row contains two elements which are the initial values of two coupled equations and there are 10000 pairs of different initial values for 10000 independent numerical calculations. At this moment I can only use loops to execute ode45 for 10000 times, which is really slow. Anybody can tell me how to cleverly parallelise this process? Many thanks in advance!

Answer 1

[Jan]

Start with optimizing the code. If e.g. the function to be integrated contains discontinuities or a lot of expensive functions to calculate constants, it is the best strategy, to improve this.

Do you have the parallel processing toolbox? Then use a PARFOR to start the integration on multiple cores. Alternatively you can start several Matlab sessions and process only parts of the 10'000 pairs of initial values. See also:

• https://www.mathworks.com/matlabcentral/fileexchange/50797-jpar-parallelizing-matlab-calculations-on-multicores-and-in-clusters-without-file-communication
• https://www.mathworks.com/matlabcentral/fileexchange/44077-batch-job
• https://www.mathworks.com/matlabcentral/fileexchange/13775-multicore-parallel-processing-on-multiple-cores

See this also: https://www.mathworks.com/matlabcentral/fileexchange/30121-parallel-computing-test--ordinary-differential-equation-