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Legendre wavelet method for numerical solutions of partial differential equations. (English) Zbl 1186.65152
The authors are concerned with the study of an orthogonal polynomial basis in two variables that are based on the Legendre polynomials on $\left[-1,1\right]$, then apply it in solving some linear second-order partial differential equations. They derive a convergence theorem concerning the expansion of a function on the square $\left[-1,1\right]×\left[-1,1\right]$ and obtain results on the accuracy of estimation for to find approximate numerical solutions to partial differential equations.
##### MSC:
 65N80 Fundamental solutions, Green’s function methods, etc. (BVP of PDE) 65N12 Stability and convergence of numerical methods (BVP of PDE) 35J25 Second order elliptic equations, boundary value problems 65T60 Wavelets (numerical methods) 65N15 Error bounds (BVP of PDE)