A New Iterative Scheme for the Solution of Partial Differential Equations Based on the Principle of Least Squares

A major shortcoming of the method of least squares, for the solution of partial differential equations, is the arbitrariness in the choice of the approximating functions. This shortcoming is eliminated by formulating the method of least squares as a variational principle and then by utilizing the it...

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Bibliographic Details
Published inSIAM journal on applied mathematics Vol. 34; no. 1; pp. 149 - 156
Main Author Kerr, Arnold D.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.1978
Subjects
A priori knowledge
Approximation
Boundary conditions
Differential equations
Flow velocity
Least squares
Magnetic fields
Mathematical functions
Ordinary differential equations
Partial differential equations
Rectangular plates
Sine function
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Summary:A major shortcoming of the method of least squares, for the solution of partial differential equations, is the arbitrariness in the choice of the approximating functions. This shortcoming is eliminated by formulating the method of least squares as a variational principle and then by utilizing the iterative scheme used in the extended Kantorovich method to generate the approximating functions. The procedure is demonstrated on an example using a one term approximation. It is found that the obtained approximation agrees very closely with the exact solution, that the convergence of the iterative process is very rapid, and that the final form of the generated solution does not depend upon the initial choice.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:0036-1399
1095-712X
DOI:10.1137/0134011