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The numerical results show the good accuracy of spectral method based on direct solvers.
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Because Chebyshev filter diagonalization avoids the need for matrix inversion it can deal with matrices and problem sizes that are presently not accessible with rational function methods based on direct or iterative linear solvers.
A simple approach to calculation of fringing field effects on beam dynamics in storage rings based on direct integration method using MATLAB ODE23 solver is presented in this paper.
The solver uses Adams method for nonstiff problems, and a method based on backward differentiation formulas for stiff problems.
It is based on nonlinear solvers, which can cope with transcendental functions of the model structure.
This solver is built based on open-source solvers OpenFOAM and LAMMPS.
The low order artificial diffusion is based on approximate Riemann solvers for hyperbolic conservation laws.
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Based on the solver proposed by Tokareva & Toro [1], a new HLLC-type Riemann solver is built.
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