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In this research work, let us focus on the construction of numerical scheme based on radial basis functions finite difference (RBF-FD) method combined with the Laplace transform for the solution of fractional order dispersive wave…

Numerical Analysis · Mathematics 2025-08-15 Hameed Ullah Jan , Marjan Uddin , Irshad Ali Shah , Salam Ullah Khan

Quantum scientific computing is to solve engineering and science problems such as simulation and optimization on quantum computers. Solving ordinary and partial differential equations (PDEs) is essential in simulations. However, existing…

Numerical Analysis · Mathematics 2026-04-28 Eunsik Choi , Jungin E. Kim , Xueling Lu , Yan Wang

In this paper, an analytic approximation method for highly nonlinear equations, namely the homotopy analysis method (HAM), is employed to solve some backward stochastic differential equations (BSDEs) and forward-backward stochastic…

Numerical Analysis · Mathematics 2018-01-25 Xiaoxu Zhong , Shijun Liao

We comment on the new trend in mathematical physics that consists of obtaining Taylor series for fabricated linear and nonlinear unphysical models by means of homotopy perturbation method (HPM), homotopy analysis method (HAM) and Adomian…

Mathematical Physics · Physics 2009-10-02 Francisco M. Fernandez

This paper is concerned with an alternative analytical solution of time-fractional nonlinear Schrodinger equation and nonlinear coupled Schrodinger equation obtained by employing fractional reduced differential transform method. The…

Numerical Analysis · Mathematics 2016-11-23 Brajesh Kumar Singh , Pramod Kumar

In the present article an endeavor is made to solve the variable order fractional diffusion equations using a powerful method viz., Homotopy Analysis method. It is demonstrated how the method can be used while solving approximately two…

General Mathematics · Mathematics 2026-04-16 Vivek Mishra , S. Das

In the present work, a new approach is proposed for finding the analytical solution of population balances. This approach is relying on idea of Homotopy Perturbation Method (HPM). The HPM solves both linear and nonlinear initial and…

Numerical Analysis · Mathematics 2017-12-27 Gurmeet Kaur , Randhir Singh , Mehakpreet Singh , Jitendra Kumar , Themis Matsoukas

In this paper, a class of high-order methods to numerically solve Functional Differential Equations with Piecewise Continuous Arguments (FDEPCAs) is discussed. The framework stems from the expansion of the vector field associated with the…

Numerical Analysis · Mathematics 2024-03-14 Gianmarco Gurioli , Weijie Wang , Xiaoqiang Yan

In this paper, Optimal Homotopy Perturbation Method (OHPM) is employed to determine an analytic approximate solutions for nonlinear MHD Jeffery-Hamel flow and heat transfer problem. The Navier-Stokes equations, taking into account Maxwell's…

Numerical Analysis · Mathematics 2015-07-13 Vasile Marinca , Remus-Daniel Ene

Nonlinear partial differential equations (PDEs) are crucial for modeling complex fluid dynamics and are foundational to many computational fluid dynamics (CFD) applications. However, solving these nonlinear PDEs is challenging due to the…

This paper presents a high-order hybrid shifted Gegenbauer integral-pseudospectral (HSG-IPS) method for solving the time-fractional Benjamin-Bona-Mahony-Burgers (FBBMB) equation. A key innovation of our approach is the transformation of the…

Numerical Analysis · Mathematics 2025-08-20 Kareem T. Elgindy

- In this paper we introduce a new method to solve fixed-delay optimal control problems which exploits numerical homotopy procedures. It is known that solving this kind of problems via indirect methods is complex and computationally…

Optimization and Control · Mathematics 2017-03-16 Riccardo Bonalli , Bruno Hérissé , Emmanuel Trélat

In the present paper invariant subspace method has been extended for solving systems of multi-term fractional partial differential equations (FPDEs) involving both time and space fractional derivatives. Further the method has also been…

Analysis of PDEs · Mathematics 2019-04-02 Sangita Choudhary , Varsha Daftardar-Gejji

In this work, we present a machine learning approach for reducing the error when numerically solving time-dependent partial differential equations (PDE). We use a fully convolutional LSTM network to exploit the spatiotemporal dynamics of…

Machine Learning · Computer Science 2020-02-11 Ben Stevens , Tim Colonius

In the present work, we use the homotopy perturbation method (HPM) to solve the Newell- Whitehead-Segel non-linear differential equations. Four case study problems of Newell-Whitehead- Segel are solved by the HPM and the exact solutions are…

General Mathematics · Mathematics 2015-03-02 S. Salman Nourazar , Mohsen Soori , Akbar Nazari-Golshan

We propose conformable Adomian decomposition method (CADM) for fractional partial differential equations (FPDEs). This method is a new Adomian decomposition method (ADM) based on conformable derivative operator (CDO) to solve FPDEs. At the…

General Mathematics · Mathematics 2017-04-11 Omer Acan , Dumitru Baleanu

The purpose of this paper is to propose a semi-analytical technique convenient for numerical approximation of solutions of the initial value problem for $p$-dimensional delayed and neutral differential systems with constant, proportional…

Classical Analysis and ODEs · Mathematics 2019-01-29 Josef Rebenda , Zdeněk Šmarda

The homotopy analysis method known from its successful applications to obtain quasi-analytical approximations of solutions of ordinary and partial differential equations is applied to stochastic differential equations with Gaussian…

Statistical Mechanics · Physics 2014-10-08 Maciej Janowicz , Filip Krzyżewski , Joanna Kaleta , Marian Rusek , Arkadiusz Orłowski

While quantum computing provides an exponential advantage in solving linear differential equations, there are relatively few quantum algorithms for solving nonlinear differential equations. In our work, based on the homotopy perturbation…

Quantum Physics · Physics 2021-12-23 Cheng Xue , Yu-Chun Wu , Guo-Ping Guo

We comment on some analytical solutions to a class of Boussinesq-like equations derived recently by means of the homotopy perturbation method (HPM). We show that one may obtain exactly the same result by means of the Taylor series in the…

Mathematical Physics · Physics 2009-07-28 Francisco M. Fernández