Convergence of the 2×2 Godunov Method for a General Resonant Nonlinear Balance Law
نویسندگان
چکیده
We introduce a generalized solution of the Riemann problem for a general resonant nonlinear balance law, and we prove the convergence of the 2 2 Godunov numerical method based on these solutions. In particular, we obtain generic conditions that guarantee a canonical structure for the elementary waves in the solution of the Riemann problem, and an interesting multiplicity of time-asymptotic wave patterns is observed and characterized.
منابع مشابه
Convergence of Numerical Method For the Solution of Nonlinear Delay Volterra Integral Equations
In this paper, Solvability nonlinear Volterra integral equations with general vanishing delays is stated. So far sinc methods for approximating the solutions of Volterra integral equations have received considerable attention mainly due to their high accuracy. These approximations converge rapidly to the exact solutions as number sinc points increases. Here the numerical solution of nonlinear...
متن کاملA SIXTH ORDER METHOD FOR SOLVING NONLINEAR EQUATIONS
In this paper, we present a new iterative method with order of convergence eighth for solving nonlinear equations. Periteration this method requires three evaluations of the function and one evaluation of its first derivative. A general error analysis providing the eighth order of convergence is given. Several numerical examples are given to illustrate the efficiency and performance of the new ...
متن کاملNonlinear Guidance Law with Finite Time Convergence Considering Control Loop Dynamics
In this paper a new nonlinear guidance law with finite time convergence is proposed. The second order integrated guidance and control loop is formulated considering a first order control loop dynamics. By transforming the state equations to the normal form, a finite time stabilizer feedback linearization technique is proposed to guarantee the finite time convergence of the system states to zero...
متن کاملA Bound on the Total Variation of the Conserved Quantities for Solutions of a General Resonant Nonlinear Balance Law
We introduce a new potential interaction functional and use it to define a new Glimm-type functional that bounds the total variation of the conserved quantities at time t > 0 by the total variation at time t = 0+ in Glimm approximate solutions of a general resonant nonlinear balance law.
متن کاملNonlinear Modeling and Investigating the Nonlinear Effects on Frequency Response of Silicon Bulk-mode Ring Resonator
This paper presents a nonlinear analytical model for micromechanical silicon ring resonators with bulk-mode vibrations. A distributed element model has been developed to describe the dynamic behavior of the micromechanical ring resonator. This model shows the nonlinear effects in a silicon ring resonator focusing on the effect of large amplitudes around the resonance frequency, material and ele...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM Journal of Applied Mathematics
دوره 55 شماره
صفحات -
تاریخ انتشار 1995