Error Estimation and Assessment of an Approximation in a Wavelet Collocation Method

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References

[1] O. V. Vasilyev and C. Bowman, “Second-Generation Wavelet Collocation Method for the Solution of Partial Differential Equations,” Journal of Computational Physics, Vol. 165, No. 2, 2000, pp. 660-693.
https://wiki.ucar.edu/download/attachments/41484400/vasilyev1.pdf
doi:10.1006/jcph.2000.6638

[2] S. Bertoluzza, “Adaptive Wavelet Collocation Method for the Solution of Burgers Equation,” Transport Theory and Statistical Physics, Vol. 25, No. 3-5, 2006, pp. 339-352.
doi:10.1080/00411459608220705

[3] T. S. Carlson, J. Dockery and J. Lund, “A Sinc-Collocation Method for Initial Value Problems,” Mathematics of Computation, Vol. 66, No. 217, 1997, pp. 215-235.
doi:10.1090/S0025-5718-97-00789-8

[4] K. Abdella, “Numerical Solution of Two-Point Boundary Value Problems Using Sinc Interpolation,” Proceedings of the American Conference on Applied Mathematics, Applied Mathematics in Electrical and Computer Engineering, 2012, pp. 157-162.

[5] A. Nurmuhammada, M. Muhammada, M. Moria and M. Sugiharab, “Double Exponential Transformation in the Sinc-Collocation Method for a Boundary Value Problem with Fourth-Order Ordinary Differential Equation,” Journal of Computational and Applied Mathematics, Vol. 162, No. 2, 2005, pp. 32-50. doi:10.1016/j.cam.2004.09.061

[6] C. Blatter, “Wavelets—Eine Einführung,” 2nd Edition, Vieweg, Wiesbaden, 2003.

[7] G. Strang, “Wavelets and Dilation Equations: A Brief Introduction,” SIAM Review, Vol. 31, No. 4, 1989, pp. 614-627. doi:10.1137/1031128

[8] Z. Shi, D. J. Kouri, G. W. Wie and D. K. Hoffman, “Generalized Symmetric Interpolating Wavelets,” Computer Physics Communications, Vol. 119, No. 2-3, 1999, pp. 194-218. doi:10.1016/S0010-4655(99)00185-X

[9] D. L. Donoho, “Interpolating Wavelet Transforms,” Technical Report 408, Department of Statistics, Stanford University, Stanford, 1992.

[10] E. Hairer and G. Wanner, “Solving Ordinary Differential Equations I: Nonstiff Problems,” 2nd Edition, Springer, Berlin, 1993.