This paper is concerned with the construction of biorthogonal multiwavelet basis in the unit interval to form a biorthogonal flatlet multiwavelet system. Next a method to calculate integer and fractional derivatives of the dual flatlet multiwavelets by multiplying some matrices is suggested. The system is then used to solve a fractional convection–diffusion equation. The biorthogonality and high vanishing moments properties of this system result in efficient and accurate solutions. Finally, numerical results for some test problems with known solutions are presented and the absolute errors are compared with the errors resulting from the other bases.
The main aim of this paper is to introduce the operational matrices of integral and fractional integral using the flatlet oblique multiwavelets. The operational matrices of integral and fractional integrals for flatlet scaling functions and wavelets are presented and are utilized to reduce the solution of the Abel integral equations of the first and the second kinds to the solution of algebraic equations. The main characteristic behind our approach in using this technique is that only a small number of flatlet oblique multiwavelets is needed to obtain a satisfactory result. Illustrative examples reveal that the present method is very effective and convenient.
In this paper, the modification of He's variational iteration method (MVIM) is developed to solve fractional integrodifferential equations with nonlocal boundary conditions. It is shown that by choosing suitable initial approximation, the exact solution obtains by one iteration. It is illustrated that the propose method is effective and has high convergency rate.
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