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Description
Ordinary differential equations (ODEs) are used for simulating and modelling real-world problems. Such problems consist of thousands to millions of equations. Nowadays, the graphical processing units are massively parallel devices that are used to accelerate many computations. The aim of this paper is to show the possibilities of solving such systems on highly parallel systems, namely GPUs.
This paper implements the Modern Taylor Series Method (MTSM) for linear problems together with state-of-the-art methods: Euler and four-stage Runge-Kutta. The implementation is done using C++ with OpenMP offloading to GPU, which compiles code for both CPU and GPU and allows the parallel utilization of GPU resources. The limitation to linear problems allows for straightforward computation of higher-order derivatives, allowing the MTSM for arbitrary precision limited only by the precision of used data types.
The modelled problem for testing methods is a signal travelling through a telegraph line, which can scale to an arbitrary number of equations. The telegraph line problem is then used to analyse the behaviour on GPU in comparison to CPU behaviour and evaluate whether GPU acceleration was beneficial.
The results show that the GPU architectures can be beneficial.