In the proposed project, parallel algorithms for solving large sparse systems of linear equations will be investigated. Such equations arise when using partial differential equations for a mathematical model describing physical processes. The algorithms will be implemented on the Convex SPP1000/XA-64 supercomputer located at the Jozef Stefan Institute. By the application of the theoretical knowledge we will thus contribute to the use of the the Convex supercomputer for solving practical computationally intensive problems. To confirm the research results, the theory will be verified by computationally intensive applications in the area of heat transfer simulation. New methods will be contributed to solving partial differential equations in parallel.