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The algorithm is based on the transverse method of lines and the reproducing kernel method.
The Method Of Lines (MOL) was used to allow higher-order temporal discretization.
The problem is solved using method of lines for partial differential equations and Galerkin's method.
The second approach employs the Crank Nicolson scheme or the method of lines for time-propagation.
For solving the McKean-Vlasov-Fokker-Planck equation (Equation 24), we have used the method of lines [72, 73].
Combining the method of lines, we formulate regularized solutions which are stably convergent to the exact solutions.
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Multidimensional transport schemes avoid splitting errors on distorted, arbitrary meshes, and method-of-lines schemes have a low computational cost because they perform reconstructions at fixed points.
The algorithm is incorporated in a finite element method-of-lines code and tested on a set of reaction diffusion systems.
All tests have been carried out using the BDF time integrator SPGEAR of the existing method-of-lines software package SPRINT.
We present a method-of-lines solution procedure for modelling charge transport and recombination in organic light-emitting diodes operating in the trap-free space-charge-limited regime.
This chapter presents the symbolic preprocessing tool symbolic preprocessing tool (SYPPRoT) of the simulation environment DIVA to apply the Method-of-Lines (MOL) approach to transform partial differential equations (PDEs) into differential algebraic equations (DAEs).
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