Search results for "equation"
showing 10 items of 4219 documents
A Spline Collocation Scheme for the Spherical Shallow Water Equations
1999
A numerical treatment of wet/dry zones in well-balanced hybrid schemes for shallow water flow
2012
The flux-limiting technology that leads to hybrid, high resolution shock capturing schemes for homogeneous conservation laws has been successfully adapted to the non-homogeneous case by the second and third authors. In dealing with balance laws, a key issue is that of well-balancing, which can be achieved in a rather systematic way by considering the 'homogeneous form' of the balance law.The application of these techniques to the shallow water system requires also an appropriate numerical treatment for the wetting/drying interfaces that appear initially or as a result of the flow evolution. In this paper we propose a numerical treatment for wet/dry interfaces that is specifically designed f…
A secular equation for the Jacobian matrix of certain multispecies kinematic flow models
2010
The 1-Harmonic Flow with Values into $\mathbb S^{1}$
2013
We introduce a notion of solution for the $1$-harmonic flow, i.e., the formal gradient flow of the total variation functional with respect to the $L^2$-distance, from a domain of $\mathbb R^m$ into a geodesically convex subset of an $N$-sphere. For such a notion, under homogeneous Neumann boundary conditions, we prove both existence and uniqueness of solutions when the target space is a semicircle and the existence of solutions when the target space is a circle and the initial datum has no jumps of an “angle” larger than $\pi$. Earlier results in [J. W. Barrett, X. Feng, and A. Prohl, SIAM J. Math. Anal., 40 (2008), pp. 1471--1498] and [X. Feng, Calc. Var. Partial Differential Equations, 37…
On finite element approximation of the gradient for solution of Poisson equation
1981
A nonconforming mixed finite element method is presented for approximation of ?w with Δw=f,w| r =0. Convergence of the order $$\left\| {\nabla w - u_h } \right\|_{0,\Omega } = \mathcal{O}(h^2 )$$ is proved, when linear finite elements are used. Only the standard regularity assumption on triangulations is needed.
OPKINE, a multipurpose program for kinetics
1991
The program OPKINE is presented for the study of reaction mechanisms and multicomponent analysis in dynamic conditions. This program is written in FORTRAN-77 for IBM 30/90 and VAX 8300 computers, and permits the simultaneous evaluation of both rate constants and initial reagent concentrations or, alternatively, rate constants and sensitivities. Up to 20 kinetic curves, with up to 400 points each, can be treated to evaluate up to 40 parameters. Integration of the system of differential equations is performed by means of the Runge–Kutta–Fehlberg method. OPKINE is provided with the Simplex, and modified versions of the Davidon–Fletcher–Powell and Gauss–Newton–Marquardt optimization methods. A …
On optimal estimates for the solutions of linear difference equations on the circle
1976
A linear difference equation arising in the proof of Moser's twist mapping theorem is solved and optimal estimates for the solution are established.
Splineapproximationen von beliebigem Defekt zur numerischen L�sung gew�hnlicher Differentialgleichungen. Teil III
1980
In the first part [5] a general procedure is presented to obtain polynomial spline approximations of arbitrary defect for the solution of the initial value problem of ordinary differential equations. The essential result is a divergence theorem in dependence of the polynomial degree and the defect of the spline functions. In this second part the convergent procedures are investigated and two convergence theorems are proved. Furthermore the question is treated, whether the convergent procedures are appropriate for the numerical solution of stiff equations. The paper is finished by a convergence theorem for a procedure producing spline approximations in a natural way by the discrete approxima…
Maximale Konvergenzordnung bei der numerischen Lösung von Anfangswertproblemen mit Splines
1982
In [10] a general procedureV is presented to obtain spline approximations by collocation for the solutions of initial value problems for first order ordinary differential equations. In this paper the attainable order of convergence with respect to the maximum norm is characterized in dependence of the parameters involved inV; in particular the appropriate choice of the collocation points is considered.
A Computational Technique for Solving Singularly Perturbed Delay Partial Differential Equations
2021
Abstract In this work, a matrix method based on Laguerre series to solve singularly perturbed second order delay parabolic convection-diffusion and reaction-diffusion type problems involving boundary and initial conditions is introduced. The approximate solution of the problem is obtained by truncated Laguerre series. Moreover convergence analysis is introduced and stability is explained. Besides, a test case is given and the error analysis is considered by the different norms in order to show the applicability of the method.