Spline-collocation with adaptive mesh grading for solving the stochastic collection equation
type: Item
instance of: scholarly article
title: Spline-collocation with adaptive mesh grading for solving the stochastic collection equation
zbMATH Open document ID: 0655.65149
DOI: 10.1016/0021-9991(88)90051-4
author: S. H. Smith
published in: Journal of Computational Physics
publication date: 1988-01-01T00:00:00Z
review text: A numerical approach is given for solving the integro-differential partial equation \[ \partial /\partial tN(mt)=\int^{m/2}_{0}N(M,t)N(m-M,t)K(M,m-M)dM- N(m,t)\int^{\infty}\quad_{0}N(M,t)K(M,m)dM \] which arises in the study of water droplet coalescence. The equation is discretized using cubic B-splines and an adaptive mesh grading, and then collocation is used to obtain a system of ordinary differential equations whose solution is approximated using well-known numerical methods. Some examples were given to illustrate the effectiveness of this approach.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 60H20
Mathematics Subject Classification ID: 65C99
Mathematics Subject Classification ID: 45K05
zbMATH DE Number: 4070268
zbMATH Keywords: stochastic collection equation
zbMATH Keywords: water droplet coalescence
zbMATH Keywords: cubic B- splines
zbMATH Keywords: adaptive mesh grading
zbMATH Keywords: collocation
reviewed by: Melvin D. Lax
MaRDI profile type: Publication
full work available at URL: 0021-9991(88)90051-4
OpenAlex ID: W2082778358
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description: scientific article; zbMATH DE number 4070268