What question did this study set out to answer?

To evaluate the stability, maximum-norm convergence order, and extrapolation accuracy of a finite difference scheme applied to linear parabolic equations with variable coefficients.

October 4, 2001Numerical Methods for Partial Differential Equations

An unconditionally stable and O(τ2 + h4) order L∞ convergent difference scheme for linear parabolic equations with variable coefficients

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Authors

ZSZhi‐zhong SunSoutheast University

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Implication

Numerical analysis demonstrates unconditional stability and fourth-order convergence for parabolic equations, highlighting broader efficacy for complex differential systems.

Key Points

To evaluate the stability, maximum-norm convergence order, and extrapolation accuracy of a finite difference scheme applied to linear parabolic equations with variable coefficients.
Applied a high-order finite difference scheme to one-dimensional linear parabolic partial differential equations featuring variable coefficients and Dirichlet boundary conditions.
Conducted analytical proofs of numerical stability and L_∞-norm convergence, and formulated an asymptotic expansion of the difference solution.
Proved that the finite difference formulation is unconditionally stable and achieves an L_∞-norm convergence order of O(τ^2 + h^4) for variable coefficient systems.
Established an asymptotic expansion that achieves an enhanced accuracy order of O(τ^4 + τ^2 h^4 + h^6) through extrapolation.

Cite This Study

Zhi‐zhong Sun (2001) studied this question.

synapsesocial.com/papers/6a7e5290b42418cb2c83e5b2 https://doi.org/10.1002/num.1030

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Implication

Numerical analysis demonstrates unconditional stability and fourth-order convergence for parabolic equations, highlighting broader efficacy for complex differential systems.

An unconditionally stable and O(τ2 + h4) order L∞ convergent difference scheme for linear parabolic equations with variable coefficients

Discussion

Member takes

Implication

Key Points

Cite This Study

An unconditionally stable and O(τ2 + h4) order L∞ convergent difference scheme for linear parabolic equations with variable coefficients

Discussion

Member takes

Implication

Key Points

Cite This Study

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