Numerical solutions to some industrial problems
<p>The particular type of industrial problem discussed is that which reduces to a hyperbolic partial differential equation with singularities.</p> <p>Two main problems are considered. The first is that of finding the position of a neutrally buoyant cable being towed behind a ship w...
| Main Author: | |
|---|---|
| Format: | Thesis |
| Published: |
1984
|
| Summary: | <p>The particular type of industrial problem discussed is that which reduces to a hyperbolic partial differential equation with singularities.</p> <p>Two main problems are considered. The first is that of finding the position of a neutrally buoyant cable being towed behind a ship which is executing horizontal transverse motions. Both the method of characteristics and a finite difference method are used to find a solution and both give satisfactory results. The algorithms are explained and the results compared.</p> <p>The second problem is concerned with the occurrence of thermal runaway when a solid medium is penetrated by a solid or immiscible liquid foreign body. Several versions, ranging in difficulty, of the problem are studied both numerically and analytically.</p> <p>There is also a study of the error in the solution when certain simple problems involving singularities are solved by finite difference methods. An expression is obtained for the generating function of the finite difference solution. The required coefficient in the generating function is expressed as a contour integral, for which an asymptotic form is obtained by the saddle point method.</p> |
|---|