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The linear Legendre mother wavelets operational matrix of integration and its application. (English) Zbl 1127.65105

Summary: The linear Legendre mother wavelets operational matrix of integration \(P\) is derived. A general procedure of forming the matrix \(P\) is given. The matrix \(P\) can be used to solve problems such as calculus of variations, differential equations, optimal control and integral equations. Illustrative examples are included to demonstrate the validity and applicability of the matrix \(P\).

MSC:

65T60 Numerical methods for wavelets
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
65K10 Numerical optimization and variational techniques
49J15 Existence theories for optimal control problems involving ordinary differential equations
49M30 Other numerical methods in calculus of variations (MSC2010)
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References:

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