A note on Legendre, Hermite, Chebyshev, Laguerre and Gegenbauer wavelets with an application on sbvps arising in real life
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Getting solution near singular point of any non-linear BVP is always tough because solution blows up near singularity. In this article our goal is to construct a general method based on orthogonal polynomial and then use different orthogonal polynomials as particular wavelets. To show importance and accuracy of our method we have solved non-linear singular BVPs with help of constructed methods and compare with exact solution. Our result shows that these method converge very fast. Convergence of constructed method is also proved in this paper. We can notice algorithm based on these methods is very fast and easy to handle. In this work we discuss multiresolution analysis for wavelets generated by orthogonal polynomials, e.g., Legendre, Chebyshev, Lagurre, Gegenbauer. Then we use these wavelets for solving nonlinear SBVPs. Wavelets are able to deal with singularity easily and efficiently.
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