Difference Methods for Initial-Value Problems

Robert D. Richtmyer; E. H. Dill

doi:10.1063/1.3060778

April 1, 1959The Journal of the Abraham Lincoln AssociationOpen Access

Difference Methods for Initial-Value Problems

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Key Points

To review and formalize finite difference methods designed to compute numerical solutions for initial-value partial differential equations.
Examined theoretical formulations that approximate continuous time-dependent differential operators using discrete grid approximations.
Analyzed mathematical criteria governing stability, error propagation, and consistency across numerical schemes.
Characterized conditions required for discrete difference equations to remain computationally stable over progressive time steps.
Demonstrated how appropriate discretization schemes prevent error amplification when approximating solutions to physical systems.

Implication

Methodological review examines finite difference schemes for initial-value problems, highlighting numerical stability and convergence criteria.

Abstract

Share Icon Share Twitter Facebook Reddit LinkedIn Reprints and Permissions Cite Icon Cite Search Site Citation Robert D. Richtmyer, E. H. Dill; Difference Methods for Initial‐Value Problems. Physics Today 1 April 1959; 12 (4): 50. https://doi.org/10.1063/1.3060778 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentPhysics Today Search Advanced Search

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Richtmyer et al. (1959) studied this question.

synapsesocial.com/papers/6a16850c0c3d638cb0bc13a4 https://doi.org/10.1063/1.3060778

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Difference Methods for Initial-Value Problems

Key Points

Implication

Abstract

Discussion

Cite This Study

Difference Methods for Initial-Value Problems

Key Points

Implication

Abstract

Discussion

Cite This Study

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