scholarly journals Simple bespoke preservation of two conservation laws

2018 ◽  
Vol 40 (2) ◽  
pp. 1294-1329 ◽  
Author(s):  
Gianluca Frasca-Caccia ◽  
Peter Ellsworth Hydon
Keyword(s):  
Finite Difference ◽  
Conservation Laws ◽  
Vries Equation ◽  
Finite Difference Methods ◽  
Nonlinear Heat Equation ◽  
Finite Difference Schemes ◽  
Simplified Approach ◽  
Numerical Tests ◽  
Difference Methods ◽  
Discrete Conservation Laws

Abstract 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 conservation laws belong to the kernel of the Euler operator, an observation that was first used recently to construct approximations symbolically that preserve two conservation laws of a given PDE. However, the complexity of the symbolic computations has limited the effectiveness of this approach. The current paper introduces some key simplifications that make the symbolic–numeric approach feasible. To illustrate the simplified approach we derive bespoke finite difference schemes that preserve two discrete conservation laws for the Korteweg–de Vries equation and for a nonlinear heat equation. Numerical tests show that these schemes are robust and highly accurate compared with others in the literature.

scholarly journals Reliable Efficient Difference Methods for Random Heterogeneous Diffusion Reaction Models with a Finite Degree of Randomness

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 206
Author(s):  
María Consuelo Casabán ◽  
Rafael Company ◽  
Lucas Jódar
Keyword(s):  
Stochastic Process ◽  
Finite Difference ◽  
Coming Out ◽  
Finite Difference Methods ◽  
Diffusion Reaction ◽  
Finite Difference Schemes ◽  
Finite Degree ◽  
Mean Square Stability ◽  
Reaction Models ◽  
Difference Methods

This paper deals with the search for reliable efficient finite difference methods for the numerical solution of random heterogeneous diffusion reaction models with a finite degree of randomness. Efficiency appeals to the computational challenge in the random framework that requires not only the approximating stochastic process solution but also its expectation and variance. After studying positivity and conditional random mean square stability, the computation of the expectation and variance of the approximating stochastic process is not performed directly but through using a set of sampling finite difference schemes coming out by taking realizations of the random scheme and using Monte Carlo technique. Thus, the storage accumulation of symbolic expressions collapsing the approach is avoided keeping reliability. Results are simulated and a procedure for the numerical computation is given.

Characteristics of finite difference methods for dispersive shallow water equations

2016 ◽  
Vol 31 (3) ◽  
Author(s):  
Zinaida I. Fedotova ◽  
Gayaz S. Khakimzyanov
Keyword(s):  
Numerical Methods ◽  
Finite Difference ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Finite Difference Methods ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Hydrodynamic Equations ◽  
Difference Methods

AbstractThe paper contains a description of the most important properties of numerical methods for solving nonlinear dispersive hydrodynamic equations and their distinctions from similar properties of finite difference schemes approximating classic dispersion-free shallow water equations.

Numerical Simulation of Diffusive Processes in Heated Cylinder Using the Finite Volume and Finite Difference Methods

2012 ◽  
Vol 326-328 ◽  
pp. 542-546 ◽  
Author(s):  
M.D. de Campos ◽  
E.C. Romão ◽  
L.F. Mendes de Moura
Keyword(s):  
Finite Difference ◽  
Finite Volume ◽  
Finite Difference Methods ◽  
Comparative Investigation ◽  
Numerical Application ◽  
Heated Cylinder ◽  
Numerical Tests ◽  
Difference Methods ◽  
Diffusive Processes ◽  
Transfer Problems

A comparative investigation of a series of numerical tests in the solution of heat transfer problems in the heated cylinder using radiation is presented. The numerical application, in steady state and cylindrical coordinates is studied through of Finite Volume and Finite Difference Methods. The numerical temperature profiles were compared with the analytical solution.

scholarly journals Finite Difference Methods for Weather Prediction in Abuja, Nigeria

2020 ◽  
pp. 915-931
Author(s):  
Jacob Emmanuel ◽  
Ogunfiditimi F.O. ◽  
Victor Alexander Okhuese ◽  
Odeyemi J. K
Keyword(s):  
Finite Difference ◽  
Weather Prediction ◽  
Finite Difference Methods ◽  
Weather Forecast ◽  
Difference Schemes ◽  
Weather Data ◽  
Finite Difference Schemes ◽  
Numerical Weather ◽  
Difference Methods ◽  
The Finite Difference Method

In this research, we have been able to simulate some finite difference schemes to predict weather trends of Abuja Station, Nigeria. By analyzing the results from these schemes, it has shown that the best scheme in the finite difference method that gives a close accurate weather forecast is the trapezoidal scheme hence we use it to simulate numerical weather data obtained from Federal Airports Authority of Nigeria (FAAN), Abuja and corresponding numerical weather data obtained by the compatible finite difference schemes, using MATLAB (R2012a) software to obtain future numerical weather trends.

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