Lectures on The Finite Element Method
by Ph. Ciarlet
Publisher: Tata Institute of Fundamental Research 1975
Number of pages: 145
Our basic aim has been to present some of the mathematical aspects of the finite element method, as well as some applications of the finite element method for solving problems in Elasticity. This is why important topics, such as curved boundaries, mixed and hybrid methods, time-dependent problems, etc..., are not covered here.
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by B. Piette - University of Durham
In these notes, we describe the design of a small C++ program which solves numerically the sine-Gordon equation. The program is build progressively to make it multipurpose and easy to modify to solve any system of partial differential equations.
by M.N. Spijker - Leiden University
Stability estimates and resolvent conditions in the numerical solution of initial value problems. Contents: Partial differential equations and numerical methods; Linear algebra; Stability in the numerical solution of differential equations; etc.
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Tutorial describing many of the standard numerical methods used in Linear Algebra. Topics include Gaussian Elimination, LU and QR Factorizations, The Singular Value Decomposition, Eigenvalues and Eigenvectors via the QR Method, etc.
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Students and professionals in the fields of mathematics, physics, engineering, and economics will find this reference work invaluable. A classic resource for special functions, standard trig, and exponential logarithmic definitions and extensions.