Zobrazeno 1 - 10
of 377
pro vyhledávání: '"65M06, 65M12"'
We study the recently-proposed hyperbolic approximation of the Korteweg-de Vries equation (KdV). We show that this approximation, which we call KdVH, possesses a rich variety of solutions, including solitary wave solutions that approximate KdV solito
Externí odkaz:
http://arxiv.org/abs/2412.17117
The main theoretical obstacle to establish the original energy dissipation laws of Runge-Kutta methods for phase-field equations is to verify the maximum norm boundedness of the stage solutions without assuming global Lipschitz continuity of the nonl
Externí odkaz:
http://arxiv.org/abs/2412.07342
One of main obstacles in verifying the energy dissipation laws of implicit-explicit Runge-Kutta (IERK) methods for phase field equations is to establish the uniform boundedness of stage solutions without the global Lipschitz continuity assumption of
Externí odkaz:
http://arxiv.org/abs/2412.07321
This study aims to construct a stable, high-order compact finite difference method for solving Sobolev-type equations with Dirichlet boundary conditions in one-space dimension. Approximation of higher-order mixed derivatives in some specific Sobolev-
Externí odkaz:
http://arxiv.org/abs/2411.18445
Robust and stable high order numerical methods for solving partial differential equations are attractive because they are efficient on modern and next generation hardware architectures. However, the design of provably stable numerical methods for non
Externí odkaz:
http://arxiv.org/abs/2411.06629
This paper presents a numerical method to solve a time-fractional Burgers equation, achieving order of convergence $(2-\alpha)$ in time, here $\alpha$ represents the order of the time derivative. The fractional derivative is modeled by Caputo-Prabhak
Externí odkaz:
http://arxiv.org/abs/2410.20192
A unified theoretical framework is suggested to examine the energy dissipation properties at all stages of additive implicit-explicit Runge-Kutta (IERK) methods up to fourth-order accuracy for gradient flow problems. We construct some parameterized I
Externí odkaz:
http://arxiv.org/abs/2410.06463
Publikováno v:
Journal of Computational Physics, 2024, 519: 113456
Explicit integrating factor Runge-Kutta methods are attractive and popular in developing high-order maximum bound principle preserving time-stepping schemes for Allen-Cahn type gradient flows. However, they always suffer from the non-preservation of
Externí odkaz:
http://arxiv.org/abs/2408.14984
Autor:
Vabishchevich, Petr N.
Numerical methods of approximate solution of the Cauchy problem for coupled systems of evolution equations are considered. Separating simpler subproblems for individual components of the solution achieves simplification of the problem at a new level
Externí odkaz:
http://arxiv.org/abs/2408.13553
We develop in this paper a new regularized flow dynamic approach to construct efficient numerical schemes for Wasserstein gradient flows in Lagrangian coordinates. Instead of approximating the Wasserstein distance which needs to solve constrained min
Externí odkaz:
http://arxiv.org/abs/2406.14870