The pointwise estimates of a conservative difference scheme for Burgers' equation
Qifeng Zhang, Xuping Wang, Zhi‐zhong Sun
Abstract
Abstract 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.
Topics & Concepts
MathematicsPointwiseNorm (philosophy)A priori and a posterioriBounded functionBurgers' equationA priori estimateApplied mathematicsMathematical analysisConvergence (economics)Nonlinear systemPartial differential equationEconomic growthEconomicsEpistemologyPhysicsPolitical scienceQuantum mechanicsPhilosophyLawDifferential Equations and Numerical MethodsNonlinear Waves and SolitonsNumerical methods for differential equations