4 papers
Numerical conservation laws of time fractional diffusion PDEs
Angelamaria Cardone, Gianluca Frasca-Caccia
The first part of this paper introduces sufficient conditions to determine conservation laws of diffusion equations of arbitrary fractional order in time. Numerical methods that sa…
Exponentially fitted methods with a local energy conservation law
Dajana Conte, Gianluca Frasca-Caccia
A new exponentially fitted version of the Discrete Variational Derivative method for the efficient solution of oscillatory complex Hamiltonian Partial Differential Equations is pro…
Optimal parameters for numerical solvers of PDEs
Gianluca Frasca-Caccia, Pranav Singh
In this paper we introduce a procedure for identifying optimal methods in parametric families of numerical schemes for initial value problems in partial differential equations. The…
Locally conservative finite difference schemes for the modified KdV equation
Gianluca Frasca-Caccia, Peter E. Hydon
Finite difference schemes that preserve two conservation laws of a given partial differential equation can be found directly by a recently-developed symbolic approach. Until now, t…