Multiscale timestepping technique for ODEs and PDEs

Abstract: The focus of this thesis is to find efficient ways of solving certain types of ODEs and PDEs. We have implemented a time upscaling method called Multiscale timestepping technique for this problems. In this method discretization of PDEs are transformed into wavelet basis, which divides the solution and the discretized differential operator into coarse scales and fine scales. Larger time steps are then used for solving the fine scale elements. In numerical experiments we show that the accuracy of the solution is maintained but the computational cost is significantly reduced compared to standard methods.