A reliable multi-resolution collocation algorithm for nonlinear Schrödinger equation with wave operator

Lei, Weidong; Ahsan, Muhammad; Ahmad, M. Omair; Nisar, Muhammad; Uddin, Zaheer

doi:10.1080/27690911.2022.2163998

Cited by 5 publications

(1 citation statement)

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“…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.

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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.

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