Cited by 18.3k
Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.
Boise State University
Publishes on Crime Patterns and Interventions, Policing Practices and Perceptions, Advanced Numerical Methods in Computational Mathematics. 35 papers and 22.9k citations.
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Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.
1. Moving boundary problems: formulation 2. Free boundary problems: formulation 3. Analytical solutions 4. Front-tracking methods 5. Front-fixing methods 6. Fixed-domain methods 7. Analytical solution of seepage problems 8. Numerical solution of free boundary problems References Author index Subject index
Approximate analytical and numerical solutions of a partial differential equation are obtained which describe the diffusion of oxygen in an absorbing medium. Essential mathematical difficulties are associated with the presence of a moving boundary which marks the furthest penetration of oxygen into the medium and also with the need to allow for an initial distribution of oxygen through the medium.
A new approach to a heat-flow problem involving a moving boundary makes use of a grid system which moves with the boundary. Two variations of the method are described. In the first, necessary interpolations are performed by using cubic splines; in the second, cubic polynomials are employed. The method smooths out irregularities in the motion of the boundary which were evident in previous calculations based on a fixed grid system.