A wavelet-based adaptive mesh refinement method for the obstacle problem

Oshagh, Mahmood Khaksar-e; Shamsi, M.; Dehghan, Mehdi

doi:10.1007/s00366-017-0559-1

Cited by 7 publications

(1 citation statement)

References 26 publications

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“…Approximation of functions in L 2 (R) in wavelet basis with elements having compact support invented roughly thirty years 25 ago has a significant impact in many areas of pure and applied mathematics, [26][27][28][29][30][31][32][33][34][35][36] physics, 37 and engineering. 38,39 This is due to the elegant role of mathematical microscopy in the analysis of smoothness of function.…”

Section: Introductionmentioning

confidence: 99%

An efficient interpolating wavelet collocation scheme for quasi‐exactly solvable Sturm–Liouville problems in ℝ+

Singh

Saha

Banik

et al. 2022

Math Methods in App Sciences

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This investigation is an attempt to obtain a highly accurate approximation of the spectrum of Sturm–Liouville problems in ℝ+ by representing the unknown solution of the model in the interpolating wavelet basis of L2false(ℝfalse). To accomplish the goal, the domain ℝ+ has been stretched to ℝ to avoid the additional care of the elements in the basis containing boundary point 0. In addition, such transformation may judiciously be utilized to eliminate (up to quadratic) the singularity of the equation. The equation in the new variable has been subsequently transformed into a generalized matrix eigenvalue problem by approximating the new (unknown) function in an appropriate (truncated) basis comprising interpolating scale functions generated by scale functions in Daubechies family. The (interpolating wavelet‐collocation) scheme developed here has been applied to some solvable and quasi‐exactly solvable Sturm–Liouville problems in ℝ+ appearing in quantum mechanical modeling in flat and curved spaces. It is observed that the approximation of eigenfunctions in the (compact support) interpolating wavelet basis obtained by using the collocation method can be reliably used to reveal a hidden spectrum of quasi‐exactly solvable Sturm–Liouville problems in ℝ+ with high accuracy.

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