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A fully Sinc‐Galerkin method for Euler–Bernoulli beam models
Author(s) -
Smith Ralph C.,
Bowers Kenneth L.,
Lund John
Publication year - 1992
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690080207
Subject(s) - mathematics , galerkin method , boundary value problem , sinc function , partial differential equation , partial derivative , cantilever , mathematical analysis , bernoulli's principle , euler's formula , finite element method , physics , engineering , thermodynamics , aerospace engineering
A fully Sinc‐Galerkin method in both space and time is presented for fourth‐order time‐dependent partial differential equations with fixed and cantilever boundary conditions. The sine discretizations for the second‐order temporal problem and the fourth‐order spatial problems are presented. Alternate formulations for variable parameter fourth‐order problems are given, which prove to be especially useful when applying the forward techniques of this article to parameter recovery problems. The discrete system that corresponds to the time‐dependent partial differential equations of interest are then formulated. Computational issues are discussed and an accurate and efficient algorithm for solving the resulting matrix system is outlined. Numerical results that highlight the method are given for problems with both analytic and singular solutions as well as fixed and cantilever boundary conditions.