For the numerical solution of time-dependent partial dierential equations, an experimental implementation of a meshfree exponential integrators is proposed. The method is of particular interest in situations where the solution of the differential equation concentrates on a small part of the computational domain which may vary in time. For the space discretization, radial basis functions with compact support are used. The time integration is performed with the exponential Rosenbrock method exprb32.
The required matrix functions are computed by Newton interpolation based on Leja points.
The integrator are fully adaptive in space and time.