A New Technique for Preserving Conservation Laws
- MathematicsFound. Comput. Math.
A new symbolic-numeric strategy for finding semidiscretizations of a given PDE that preserve multiple local conservation laws and it is shown that the new technique is practicable for PDEs with three dependent variables.
Exponentially fitted methods that preserve conservation laws
- MathematicsCommun. Nonlinear Sci. Numer. Simul.
Optimal parameters for numerical solvers of PDEs
- Mathematics, Computer ScienceArXiv
A procedure for identifying optimal methods in parametric families of numerical schemes for initial value problems in partial differential equations maximizes accuracy by adaptively computing optimal parameters that minimize a defect-based estimate of the local error at each time-step is introduced.
Numerical conservation laws of time fractional diffusion PDEs
- MathematicsFractional Calculus and Applied Analysis
This paper introduces sufficient conditions to determine conservation laws of diffusion equations of arbitrary fractional order in time. Numerical methods that satisfy discrete counterparts of these…
Arbitrary high-order linear structure-preserving schemes for the regularized long-wave equation
- Computer ScienceApplied Numerical Mathematics
Exponentially fitted methods with a local energy conservation law
A new exponentially fitted version of the Discrete Variational Derivative method for the efficient solution of oscillatory complex Hamiltonian Partial Differential Equations is proposed. When applied…
Complete Classification of Local Conservation Laws for Generalized Cahn-Hilliard-Kuramoto-Sivashinsky Equation
In the present paper we consider nonlinear multidimensional Cahn–Hilliard and Kuramoto– Sivashinsky equations that have many important applications in physics and chemistry, and a certain natural…
Complete Classification of Local Conservation Laws for Generalized Kuramoto–Sivashinsky Equation
For an arbitrary number of spatial independent variables we present a complete list of cases when the generalized Kuramoto–Sivashinsky equation admits nontrivial local conservation laws of any order,…
Data-Driven Soliton Solutions and Model Parameters of Nonlinear Wave Models Via the Conservation-Law Constrained Neural Network Method
- Computer ScienceSSRN Electronic Journal
SHOWING 1-10 OF 51 REFERENCES
Simple bespoke preservation of two conservation laws
- MathematicsIMA Journal of Numerical Analysis
Conservation laws are among the most fundamental geometric properties of a partial differential equation (PDE), but few known finite difference methods preserve more than one conservation law. All…
Locally conservative finite difference schemes for the modified KdV equation
- MathematicsJournal of Computational Dynamics
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, this has been used…
Bespoke finite difference schemes that preserve multiple conservation laws
- Computer Science
A new systematic method for discretizing a PDE, so as to preserve the local form of multiple conservation laws, is presented and is applied to the Korteweg–de Vries equation to find novel explicit and implicit schemes that have finite difference analogues of its first and second conservation laws.
Finite difference solutions of the nonlinear Schrödinger equation and their conservation of physical quantities
The solutions of the nonlinear Schrodinger equation are of great importance for ab initio calculations. It can be shown that such solutions conserve a countable number of quantities, the simplest…
Backward error analysis for multisymplectic discretizations of Hamiltonian PDEs
- MathematicsMath. Comput. Simul.
Preserving energy resp. dissipation in numerical PDEs using the "Average Vector Field" method
- Mathematics, PhysicsJ. Comput. Phys.
Characteristics of Conservation Laws for Difference Equations
- MathematicsFound. Comput. Math.
The converse of Noether’s Theorem for difference equations is established, the conservation laws in the infinite family generated by Rasin and Schiff are distinct, and all five-point conservation laws for the potential Lotka–Volterra equation are obtained.
A General Framework for Deriving Integral Preserving Numerical Methods for PDEs
- Mathematics, Computer ScienceSIAM J. Sci. Comput.
A general procedure for constructing conservative numerical integrators for time-dependent partial differential equations is presented. In particular, linearly implicit methods preserving a time…
Dissipative or Conservative Finite Difference Schemes for Complex-Valued Nonlinear Partial Different
Abstract We propose a new procedure for designing finite-difference schemes that inherit energy conservation or dissipation property from complex-valued nonlinear partial differential equations…
Conservation laws of partial difference equations with two independent variables
This paper introduces a technique for obtaining the conservation laws of a given scalar partial difference equation with two independent variables. Unlike methods that are based on Nother's theorem,…