ADAPTED NUMERICAL METHODS FOR ADVECTION DIFFUSION PROBLEMS

We present exponentially fitted two step peer methods for the numerical solution of systems of ordinary differential equations having oscillatory solutions (2; 3). Such equations arise for example in the semi-discretization in space of advection-diffusion problems whose solution exhibits an oscillatory behaviour, such as the Boussinesq equation (1). Exponentially fitted methods are able to exploita-prioriknowninformationaboutthequalitativebehaviourofthesolutionin order to efficiently furnish an accurate solution. Moreover peer methods are very suitable for a parallel implementation, which may be necessary when the number ofspatialpointsincreases. Theeffectivenessofthisproblem-orientedapproachis shown through numerical tests on well-known problems. References [1] A. Cardone, R. D’Ambrosio, B. Paternoster. (2017). Exponentially fitted IMEX methods for advectiondiffusion problems, J. Comput. Appl. Math. (316), 100–108. [2] D. Conte, R. D’Ambrosio, M. Moccaldi, B. Paternoster. (2018). Adapted explicit two-step peer methods, J. Numer. Math., in press. [3] D. Conte, L. Moradi, B. Paternoster. (2017). Adapted implicit two-step peer methods, in preparation