We study numerically a class of quasilinear Schrödinger equations using the Strang splitting method. For these particular models, we can prove convergence of our approximation by adapting the work of Lubich [30] for a Lie theoretic approach to the continuous time approximation and Sobolev-based well-posedness results of the second author with J. Metcalfe and D. Tataru in order to model small in...

We present a numerical method, based on a three-dimensional finite volume wave-propagation algorithm, for solving the Vlasov equation in a full six-dimensional (three spatial coordinates, three velocity coordinates) case in length scales comparable to the size of the Earth’s magnetosphere. The method uses Strang splitting to separate propagation in spatial and velocity coordinates, and is secon...

We consider pricing options in a jump-diffusion model which requires solving a partial integro-differential equation. Discretizing the spatial direction with a fourth order compact scheme leads to a linear system of ordinary differential equations. For the temporal direction, we utilize the favorable boundary value methods owing to their advantageous stability properties. In addition, the resul...

Abstract In this paper, we construct and analyze a new dynamical low-rank integrator for second-order matrix differential equations. The method is based on combination of the projector-splitting introduced in Lubich Oseledets (BIT 54(1):171–188, 2014. https://doi.org/10.1007/s10543-013-0454-0 ) Strang splitting. We also present variant which tailored to semilinear problems.

Veronica Strang, Water Beings: From Nature Worship to the Environmental Crisis. London: Reaktion Books, 2023. 280 pp.; 126 color plates; 5 halftones. US$45.00.

We show that the Strang splitting method applied to a diffusion-reaction equation with inhomogeneous general oblique boundary conditions is of order two when diffusion solved Crank-Nicolson method, while reduction occurs in if using other Runge-Kutta schemes or even exact flow itself for part. prove these results source term only depends on space variable, an assumption which makes scheme equiv...

Angiogenesis – the process by which new blood vessels grow into a tissue from surrounding parent vessels – is an important process in many areas of medicine. Here we consider the numerical simulation of a PDE model of tumor-induced angiogenesis. It contains convection (migration), diffusion and reaction terms. Despite the restriction to one specific model, the observations should also be releva...

This paper introduces optimally-blended quadrature rules for isogeometric analysis and analyzes the numerical dispersion of the resulting discretizations. To quantify the approximation errors when we modify the inner products, we generalize the Pythagorean eigenvalue theorem of Strang and Fix. The proposed blended quadrature rules have advantages over alternative integration rules for isogeomet...

Reaction-Advection-Diffusion problems occurring in Air Pollution Models have very stiff reaction terms and moderately stiff vertical mixing (diffusion and cloud transport) terms which both should be integrated implicitly in time. Standard implicit time stepping is by far too expensive for this type of problems whereas widely used splitting techniques may lead to unacceptably large errors for fa...

This present study develops a 2-D numerical scheme to simulate the velocity and depth on the actual terrain by using shallow water equations. The computational approach uses the HLL scheme as a basic building block, treats the bottom slope by lateralizing the momentum flux, then refines the scheme using the Strang splitting to deal with the frictional source term. Besides, a decoupled algorithm...