Numerical solutions of higher order boundary value problems via wavelet approach

Arifeen, Shams Ul; Haq, Sirajul; Ghafoor, Abdul; Ullah, Asad; Chaipanya, Parin

doi:10.1186/s13662-021-03495-6

Cited by 13 publications

(6 citation statements)

References 24 publications

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“…Olumide et al, (2020) proposed 7 th order continuous block methods for approximate solution of sixth-order BVPs. Further, Arifeen et al, (2021) developed Haar wavelet method for the approximate solutions of higher order linear and nonlinear BVPs. Tsetimi et al, (2022) considered modified variational iteration method by using Chebyshev polynomials to solved 12 th order BVPs.…”

Section: Introductionmentioning

confidence: 99%

Maclaurin Series Solution for Seventh Order Boundary Value Problems

Bello,

Mutawakilu,

Aminu

2023

IJSGS

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Maclaurin series expansion which is taught at undergraduate levels and which has been previously used for the solution of initial value problem is successfully used in this paper for the solutions of seventh-order boundary value problems. The governing equation defined between boundary points 0 and 1is differentiated to get high order derivatives and the assumed solution is expanded in Maclaurin series then, the boundary conditions at x=1 are utilized to determined unknown coefficients. The method is simple and the numerical results displayed on the tables were found to be in good agreement with the solution and even better than some existing results in the literature. This agreement is also confirmed from the figures were the graph of exact solution and approximate solution overlap.

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Section: Introductionmentioning

confidence: 99%

Maclaurin Series Solution for Seventh Order Boundary Value Problems

Bello,

Mutawakilu,

Aminu

2023

IJSGS

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“…Another mathematical model concerning fluid flow through a porous and stretching sheet is analytically simulated, including mass transfer, thermal radiation, and Hall current [28]. Detailed mathematical approaches concern hybrid nanofluid flow energy transfer through a permeable vertically rotating surface [29] and other numerical models of heat transfer, including convergence of the studied models [30,31]. These nanofluids have demonstrated promising capabilities in enhancing thermal conductivity and heat transfer efficiency.…”

Section: Introductionmentioning

confidence: 99%

Study of Heat Recovery Equipment for Building Applications

Popescu,

Catalina

2023

Buildings

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Nowadays, heat exchangers find widespread use across various applications in different fields, particularly in the field of heat recovery. This paper provides a detailed explanation of a plate heat exchanger counter-flow model developed in Simulink/Matlab. Water was employed in simulations for both circuits, although the thermal properties of other fluids can be investigated by modifying them. The “Tanks in series” method was used for simulation purposes. The developed model enables users to explore the impact of various parameters on heat exchanger functionality, such as altering the number of plates, the material or thickness of the plates, and the nature of thermal agents (gaseous or liquid). These models play a crucial role not only in simulating and sizing heat exchangers but also in achieving parametric optimization. Parameter variations can be employed to examine the operation of existing equipment under conditions different from their design specifications. The Simulink/Matlab proposed model, featuring a variable number of finite volumes to ensure high accuracy, was compared to the classical design method for plate heat exchangers. The results revealed good accuracy, with relative errors for heat transfer rate remaining below 2.6%. This research also considered the study of the number of finite volumes necessary for achieving accurate results. For the 40 finite volumes model, the relative error for heat transfer rate is less than 10%. Dividing the mesh into 50 finite volumes along the fluid flow direction resulted in relative errors ranging from 1.6% to 1.7%, indicating that a finer mesh was not necessary. To validate the conceived model, experimental data from the literature were compared. The relative errors for heat transfer rate between the Matlab/Simulink model’s results and experimental data ranged from 1.58% to 11.92%, demonstrating a strong agreement between the conceived model and the experimental values.

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“…Ali et al solved higher order BVPs using the optimal homotopy asymptotic method (OHAM) in [16]. Other scholars who tried di erent methodologies for the solution of higher order BVPs can be seen in [17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Extended Residual Power Series Algorithm for Boundary Value Problems

Qayyum

Fatima

Sohail

et al. 2022

Mathematical Problems in Engineering

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In this article, modification of the residual power series method (RPSM) is proposed for higher order boundary value problems (BVPs). The proposed algorithm is tested against various linear and nonlinear BVPs of orders nine up to thirteen. For the efficiency check of RPSM, obtained series solutions are compared with other available results in the literature. Analysis indicates that RPSM is better in terms of accuracy as compared to other mentioned schemes. As RPSM is applicable to BVPs without linearization, discretization, and perturbation, hence practically it is the best suitable solution tool for more complex BVPs in science and engineering.

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Numerical solutions of higher order boundary value problems via wavelet approach

Cited by 13 publications

References 24 publications

Maclaurin Series Solution for Seventh Order Boundary Value Problems

Maclaurin Series Solution for Seventh Order Boundary Value Problems

Study of Heat Recovery Equipment for Building Applications

Extended Residual Power Series Algorithm for Boundary Value Problems

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