The pointwise estimates of a conservative difference scheme for Burgers' equation | Zendy

Zhang Qifeng | Zendy; Wang Xuping | Zendy; Sun Zhizhong | Zendy

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The pointwise estimates of a conservative difference scheme for Burgers' equation

Author(s) -

Zhang Qifeng,

Wang Xuping,

Sun Zhizhong

Publication year - 2020

Publication title -

numerical methods for partial differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.901

H-Index - 61

eISSN - 1098-2426

pISSN - 0749-159X

DOI - 10.1002/num.22494

Subject(s) - mathematics , pointwise , norm (philosophy) , a priori and a posteriori , bounded function , burgers' equation , a priori estimate , mathematical analysis , convergence (economics) , nonlinear system , partial differential equation , philosophy , epistemology , political science , law , economics , economic growth , physics , quantum mechanics

In this article, we are concerned with the numerical analysis of a nonlinear implicit difference scheme for Burgers' equation. A priori estimation of the analytical solution is provided in the sense of L ∞ ‐norm when the initial value is bounded in H 1 ‐norm. Conservation, boundedness, and unique solvability are proved at length. Inspired by the method of the priori estimation for the analytical solution, we prove the convergence and stability of the difference scheme in L ∞ ‐norm. Finally, numerical examples are carried out to verify our theoretical results.

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