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LEIBNITZ-HAAR WAVELET COLLOCATION METHOD FOR THE NUMERICAL SOLUTION OF NONLINEAR FREDHOLM INTEGRAL EQUATIONS

, 2016
In this work, we present a numerical solution of nonlinear fredholm integral equations using Leibnitz-Haar wavelet collocation method. Properties of haar wavelet and its operational matrix is utilized to convert into a system of algebraic equations ...
S. C. Shiralashetti *, R. A. Mundewadi
core   +1 more source

Phase‐Lag Integro‐Partial Differential Equation: Local and Nonlocal Solutions

Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.
Nonlocal information, such as material deformation, genetic genes, or the history of the disease, are essential as they provide us with additional details that increase the numerical solution’s accuracy. With the help of the phase delay, we may also predict the future of the phenomena we are researching.
Sameeha Ali Raad, Ivan Giorgio
wiley   +1 more source

A Haar wavelet-based scheme for finding the control parameter in nonlinear inverse heat conduction equation

Open Physics, 2021
In this article, a hybrid Haar wavelet collocation method (HWCM) is proposed for the ill-posed inverse problem with unknown source control parameters. Applying numerical techniques to such problems is a challenging task due to the presence of nonlinear ...
Ahsan Muhammad, Lin Shanwei, Ahmad Masood, Nisar Muhammad, Ahmad Imtiaz, Ahmed Hijaz, Liu Xuan   +6 more
doaj   +1 more source

Fractional Dynamics of Nonlinear Liquid Dispersion Pattern Drops: A Robust Analytical Study of Modulation Instability and Compacton Structures

Computational and Mathematical Methods, Volume 2026, Issue 1, 2026.
Nonlinear dispersion phenomena in liquid media often lead to the formation of localized structures such as compact wave packets and dispersion drops. The present investigation demonstrates that the proposed analytical framework yields accurate approximate solutions, successfully captures compacton‐like structures, and clearly reveals the critical ...
Yogeshwari F. Patel, Mohammad Izadi, Hany M. Ahmed, Rajesh Kumar   +3 more
wiley   +1 more source

An Efficient Approach for Mixed Neutral Delay Differential Equations

Computation
In this paper, neutral delay differential equations, which contain constant and proportional terms, termed mixed neutral delay differential equations, are solved numerically.
Rupal Aggarwal, Giriraj Methi, Ravi P. Agarwal, Basharat Hussain   +3 more
doaj   +1 more source

Wavelet Collocation Method Based on Biorthogonal Flatlet Multiwavelet and Its Application in Solving the Singular BVPs

International Journal of Differential Equations, Volume 2026, Issue 1, 2026.
The main focus of our work is to provide a computationally efficient approximate algorithm for finding a numerical solution of singular boundary value problems (SBVPs). For this purpose, we apply a biorthogonal flatlet multiwavelet collocation method (BFMCM) to solve numerically. This is performed by approximating functions using a BFMCM.
Maryam Mohseni, Davood Rostamy, Md. Kamrujjaman   +2 more
wiley   +1 more source

Existence and Uniqueness of Nonlinear Volterra Integral Equations With Variable Fractional Order in Fréchet Spaces via a Frigon−Granas Fixed Point Approach

International Journal of Differential Equations, Volume 2026, Issue 1, 2026.
This paper investigates the existence and uniqueness of solutions to nonlinear Volterra integral equations of variable fractional order in Fréchet spaces. The variable‐order fractional derivative is considered in the Riemann–Liouville sense, which extends classical approaches and is central to the paper’s novelty.
Mohamed Telli, Benoumran Telli, Mohammed Said Souid, K. Sudarmozhi, Joshua Kiddy K. Asamoah, Khalil Ezzinbi   +5 more
wiley   +1 more source

A wavelet-based collocation approach for solving chlorine transport model

Boundary Value Problems
This study provides a unified framework for analyzing the two-dimensional chlorine transport model in pipes, governed by a second-order partial differential equation with complex boundary conditions.
J. Suganthi, Saurabh Chandra Maury
doaj   +1 more source

A higher-order collocation technique based on Haar wavelets for fourth-order nonlinear differential equations having nonlocal integral boundary conditions

Alexandria Engineering Journal
This article encounters the use of two wavelet methods, namely the collocation method based on Haar wavelets (CMHW) and the higher-order collocation method based on Haar wavelets (HCMHW), to solve linear and nonlinear fourth-order differential equations ...
Muhammad Ahsan, Weidong Lei, Amir Ali Khan, Masood Ahmed, Maher Alwuthaynani, Ayesha Amjad   +5 more
doaj   +1 more source

Solution of Time‐Fractional Coupled Burgers Equations by the Yang Transform Adomian Decomposition Method

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
In this paper, the Yang transform Adomian decomposition method (YTADM) is employed in the solution of nonlinear time‐fractional coupled Burgers equations. The technique solves the fractional and nonlinear terms successfully via the Adomian decomposition of the Yang transform.
Mustafa Ahmed Ali, Mehmet Merdan, Yeou Jiann Lim   +2 more
wiley   +1 more source