The Analysis of a Variable Step, Variable Coefficient Linear Multistep Method for Solving a Singular Integro–Differential Equation Arising from the Diffusion of Discrete Particles in a Turbulent Fluid
- 1 April 1979
- journal article
- research article
- Published by Oxford University Press (OUP) in IMA Journal of Applied Mathematics
- Vol. 23 (3) , 373-388
- https://doi.org/10.1093/imamat/23.3.373
Abstract
A singular integro-differential equation representing a particle moving in a turbulent fluid is studied. An existence and uniqueness result and an analytic solution (for a special case) is given. A variable step, variable coefficient finite difference method is derived through product integration. The usual convergence lemma is generalized and this permits an elegant convergence proof. Numerical stability is discussed and an approximate criterion for absolute stability is derived. Simple numerical results are given.Keywords
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