Meshfree exponential integrators

For the numerical solution of time-dependent partial dierential equations, a class ofmeshfree exponential integrators is proposed. These methods are of particular interest in situationswhere the solution of the dierential equation concentrates on a small part of the computationaldomain which may vary in time. For the space discretization, radial basis functions with compactsupport are suggested. The reason for this choice are stability and robustness of the resultinginterpolation procedure. The time integration is performed with an exponential Rosenbrock method.The required matrix functions are computed by Newton interpolation based on Leja points. Theproposed integrators are fully adaptive in space and time. Numerical examples that illustrate therobustness and the good stability properties of the method are included.