Convergence for PDEs with an arbitrary odd order spatial derivative term
arXiv:1712.022956 citationsh-index: 6
Originality Synthesis-oriented
AI Analysis
Provides theoretical convergence guarantees for numerical schemes used in solving a class of PDEs, but the results are incremental as they extend known analysis to a specific term.
The paper computes convergence rates for finite difference θ-schemes applied to linear PDEs with arbitrary odd-order spatial derivative terms, proving first- or second-order convergence depending on initial data smoothness.
We compute the rate of convergence of forward, backward and central finite difference $θ$-schemes for linear PDEs with an arbitrary odd order spatial derivative term. We prove convergence of the first or second order for smooth and less smooth initial data.