A Haar wavelets based approximation for nonlinear inverse problems influenced by unknown heat source

Ahsan, Muhammad; Haq, Khawaja Shams‐ul; Li, Xuan; Lone, Showkat Ahmad; Nisar, Muhammad

doi:10.1002/mma.8655

Cited by 7 publications

(3 citation statements)

References 60 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The advantage of this method is that it is a non-continuous step and helps analyze images that suffer from spatial discontinuities. The primary wave of the Haar wave can be calculated and determined from (1) [29]- [31]:…”

Section: Haar Waveletmentioning

confidence: 99%

A new approach to develop biometric fingerprint using human right thumb fingernail

Al-Sultan

Alhialy

Alkhaled

et al. 2023

IJEECS

View full text Add to dashboard Cite

In this article, we analyzed the structure of human nails to develop a modern biometric authentication system based on the nail bed and finger lunula. The results of the studies on the collected images proved that each fingernail has distinctive characteristics in terms of the length and width of the nail and the lunula, even identical twins. We focused on the fingernail of the right thumb because of its large size and the accuracy and clarity of the nail. The mediation of the indicative points on the nail bed and on the lunula was used to form the pentagonal structure and use it as a region of interest. Then an ensemble independent component analysis, principal component analysis, haar wavelet, and scale invariant feature transformation, were used. Later we classified these algorithms using support vector machine and Naive Bayes techniques, the performance of each algorithm was analyzed by feature extraction with two classifiers. This study was conducted on 100 participants and showed that this new method could be used as a biometric identification system for humans. There was no similarity in results for all verified samples.

show abstract

Section: Haar Waveletmentioning

confidence: 99%

A new approach to develop biometric fingerprint using human right thumb fingernail

Al-Sultan

Alhialy

Alkhaled

et al. 2023

IJEECS

View full text Add to dashboard Cite

show abstract

“…Additionally, challenging fractional differential and integral equations are deciphered by CMHW as well [37][38][39]. Different other types of direct and inverse problems are also solved by the CMHW, which are reported in [40][41][42][43].…”

Section: Introductionmentioning

confidence: 99%

A higher-order collocation method based on Haar wavelets for integro-differential equations with two-point integral condition

Ahsan,

Lei,

Alwuthaynani

et al. 2023

Phys. Scr.

Self Cite

View full text Add to dashboard Cite

In this article, the higher-order Haar wavelet collocation method (HCMHW) is investigated to solve linear and nonlinear integro-differential equations (IDEs) with two types of conditions: simple initial condition and the point integral condition. We reproduce and compare the numerical results of the conventional Haar wavelet collocation method (CMHW) with those of HCMHW, demonstrating the superior performance of HCMHW across various conditions. Both methods effectively handle different types of given conditions. However, numerical results reveal that HCMHW exhibits a faster convergence rate than CMHW. To address nonlinear IDEs, we employ the quasi-linearization technique. The computational stability of both methods is evaluated through various experiments. Additionally, the article provides examples to illustrate the overall performance and accuracy of HCMHW compared to CMHW for both linear and nonlinear IDEs.

show abstract

“…The right side unknown boundary condition is accurately measured by HWCM in a nonlinear inverse problem [14]. Apart from inverse problems, the HWCM is also applied to solve linear and nonlinear applied problems in [42][43][44][45][46][47][48] and the references therein.…”

Section:  Introductionmentioning

confidence: 99%

A wavelet-based collocation technique to find the discontinuous heat source in inverse heat conduction problems

et al. 2022

Self Cite

View full text Add to dashboard Cite

This paper is devoted to an inverse problem of determining discontinuous space-wise dependent heat source in a linear parabolic equation from the measurements at the ﬁnal moment. In the existing literature, a considerable accurate solution to the inverse problems with unknown space-wise dependent heat source is impossible without introducing any type of regularization method but here we have determine the unknown discontinuous space-wise dependent heat source acutely using Haar wavelet collocation method (HWCM) without applying the regularization technique. This HWCM is based on ﬁnite-diﬀerence and Haar wavelets approximation to the inverse problem. In contrast to other numerical techniques, in HWCM, we use Haar functions that create a well-conditioned system of algebraic equations. The proposed method is stable and convergent because the numerical solution converges to the exact solution without observing any diﬃculty. Finally, some numerical examples are presented to verify the validity of the HWCM for diﬀerent cases of source term.

show abstract

A Haar wavelets based approximation for nonlinear inverse problems influenced by unknown heat source

Cited by 7 publications

References 60 publications

A new approach to develop biometric fingerprint using human right thumb fingernail

A new approach to develop biometric fingerprint using human right thumb fingernail

A higher-order collocation method based on Haar wavelets for integro-differential equations with two-point integral condition

A wavelet-based collocation technique to find the discontinuous heat source in inverse heat conduction problems

Contact Info

Product

Resources

About