Titlebook: Numerical Methods for Partial Differential Equations; Gwynne A. Evans,Jonathan M. Blackledge,Peter D. Ya Textbook 2000 Springer-Verlag Lon

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Numerical Methods for Partial Differential Equations

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Finite Differences and Parabolic Equations,imated by a set of algebraic equations, for the function values at the nod al points. In order to perform this discretisation, expressions for such terms as at typical grid points are required in terms of the ϕ values at neighbouring grid points.

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Hyperbolic Equations and Characteristics,of a method of solution. The method is based on using finite differences along the characteristic curves which form a natural grid. This will be covered in Section 3.3 and a slightly different derivation to that in Chapter 1 will be given, as this approach is informative in its own right.

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1615-2085 EMS RATHER THAN THE THEORETICAL BACKGROUND * CONTAINS NUMEROThe subject of partial differential equations holds an exciting and special position in mathematics. Partial differential equations were not consciously created as a subject but emerged in the 18th century as ordinary differential equations

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Background Mathematics,tion will form a basis for study from a numerical point of view for the same reason as they did in the analytic case. That is, the three equations are the canonical forms to which any quasi-linear second order equation may be reduced using the characteristic transformation.

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Finite Elements for Partial Differential Equations,ion may not be continuous where the elements fit together. The ultimate accuracy of the solution is dependent upon the number and size of the elements, and the types of approximate function used within the elements.

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