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Article
Investigation of the wavelet method impact on the mathematical model of global warming effects on marine ecosystems
In this work, the Haar wavelet collocation method (HWCM) is used to study the mathematical model of Global warming that impacts the marine ecosystem. The sustainable growth of the environment is only achieved ...
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Article
Numerical solution for a fractional operator-based mathematical model of a brain tumour
Intricate mathematical models of malignant growths have been devised, particularly for solid tumours, whose growth is predominantly driven by cellular proliferation. The most severe type of brain cancer, gliom...
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Article
Open AccessNumerical approximation of the typhoid disease model via Genocchi wavelet collocation method
In this paper, we have considered the fractional typhoid disease model and obtained the numerical approximation of the model via the innovative wavelet scheme called the Genocchi wavelet collocation method (GW...
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Article
A numerical study of the evolution of smoking habit model through Haar wavelet technique
The prosperity of a nation reflects many parameters such as natural resources, literacy, and population. Nowadays national wealth is its population’s health, and many bad habits affect the population. Smoking ...
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Article
Open AccessNumerical solution of fractional PDEs through wavelet approach
To solve fractional partial differential equations (FPDEs) under various physical conditions, this study developed a novel method known as the Hermite wavelet method employing the functional integration matrix...
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Article
Open AccessTime-varying stretching velocity analysis for an unsteady flow of Williamson fluid by Hermite wavelet
This study investigates unsteady velocity \({U}_{w}=\xi x/t\) U ...
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Article
Open AccessA numerical study on the nonlinear fractional Klein–Gordon equation
This article helps to develop a numerical approach based on Fibonacci wavelets for solving fractional Klein-Gordan equations (FKGEs). The FKGEs are solved with Caputo-type fractional derivative. Using the defi...
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Article
Open AccessA new graph theoretic analytical method for nonlinear distributed order fractional ordinary differential equations by clique polynomial of cocktail party graph
In this paper, we presented a new analytical method for one of the rapidly emerging branches of fractional calculus, the distributed order fractional differential equations (DFDE). Due to its significant appli...
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Article
Numerical solution of a modified epidemiological model of computer viruses by using Fibonacci wavelets
In the present article, we introduced the innovative Fibonacci wavelet method to compute the approximate solution of the nonlinear modified epidemiological model of computer viruses with the help of an operati...
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Article
Numerical solution of some stiff systems arising in chemistry via Taylor wavelet collocation method
This paper presents the innovative Taylor wavelet collocation method (TWCM) for the stiff systems arising in chemical reactions. In this technique, first, we generated the functional matrix of integration (FMI...
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Article
Open AccessFibonacci wavelets operational matrix approach for solving chemistry problems
The key idea and contribution of this study are to present the innovative functional matrix approach for solving the two chemical, mathematical problems such as the absorption of
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Article
Fibonacci wavelet collocation method for the numerical approximation of fractional order Brusselator chemical model
This research study’s primary goal is to create an efficient wavelet collocation technique to resolve a kind of nonlinear fractional order systems of ordinary differential equations that arise in the modeling ...
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Article
Fibonacci wavelets-based numerical method for solving fractional order (1 + 1)-dimensional dispersive partial differential equation
In this study, third-order fractional (1 + 1)-dimensional dispersive partial differential equations are numerically solved using the generalized fractional-order Fibonacci wavelet functions. Fibonacci wavelet ...
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Article
Bernoulli Wavelets Numerical Approach for the Nonlinear Klein–Gordon and Benjamin–Bona–Mahony Equation
The paper is concerned with different classes of partial differential equations (PDEs), such as nonlinear Benjamin–Bona–Mahony and Klein–Gordon equations with variable coefficients. We developed a new integra...
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Article
A novel approach for multi dimensional fractional coupled Navier–Stokes equation
This study proposed a new scheme called the Hermite wavelet method (HWM) to find the numerical solutions to the multidimensional fractional coupled Navier–Stokes equation (NSE). This approach is based on the H...
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Article
A Study on the Non-Linear Murray Equation Through the Bernoulli Wavelet Approach
In this paper, we developed the operational matrices of integration based on the Bernoulli wavelets and proposed the novel technique known as the Bernoulli wavelet collocation method (BWCM) for extended bounda...
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Article
Open AccessApplications of the Bernoulli wavelet collocation method in the analysis of MHD boundary layer flow of a viscous fluid
This study focuses on the flow of viscous, electrically conducting incompressible fluid over a stretching plate. The Falkner–Skan equation is a nonlinear, third-order boundary value problem. No closed-form sol...
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Article
Applications of Bernoulli wavelet collocation method in the analysis of Jeffery–Hamel flow and heat transfer in Eyring–Powell fluid
In this article, we developed the new functional matrix of integration using the Bernoulli wavelet and proposed a novel technique called the Bernoulli wavelet collocation method (BWCM). The main intention of t...
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Article
A solution of coupled nonlinear differential equations arising in a rotating micropolar nanofluid flow system by Hermite wavelet technique
In this article, the two-dimensional micropolar rotating nanofluid between two parallel plates under Hall's influence can be solved using the Hermite wavelet technique (HWT). The nanofluid flow between two par...
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Article
Application of Hermite Wavelet Method and Differential Transformation Method for Nonlinear Temperature Distribution in a Rectangular Moving Porous Fin
We developed a novel technique called the Hermite wavelet collocation method (HWM) in the current work. Here, the variation of nonlinear temperature in a permeable moving fin of the rectangular domain is studi...
