Quarter-sweep successive over-relaxation approximation to the solution of porous medium equations by Chew, Jackel Vui Lung, Elayaraja Aruchunan, Andang Sunarto, Jumat Sulaiman

“…Several initial-boundary value problems of the porous medium equation are solved to illustrate the efficiency of the proposed method. …”
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Multiple solutions of Cu-C6H9NaO7 and Ag-C6H9NaO7 nanofluids flow over nonlinear shrinking surface by Lund, Liaquat Ali, Omar, Zurni, Khan, Ilyas, Dero, Sumera

“…The governing nonlinear equations incorporating the effects of the viscous dissipation are transformed into boundary value problems (BVPs) of ordinary differential equations (ODEs) by using appropriate similarity transformations. …”
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Numerical solution of nonlinear diffusion in one dimensional porous medium using hybrid SOR method by Jackel Vui Lung Chew, Elayaraja Aruchunan, Andang Sunarto, Jumat Sulaiman

“…Some numerical experiments are delivered using initial-boundary value problems to show the superiority of the proposed method against some existing numerical methods.…”
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Heat transfer study of convective fin with temperature-dependent internal heat generation by hybrid block method by Alkasassbeh, Mohammad, Omar, Zurni, Mebarek-Oudina, Fateh, Raza, Jawad, Chamkha, Ali

“…Purpose: In this study, an implicit one‐step hybrid block method using two off‐step points involving the presence of a third derivative for solving second‐order boundary value problems are subjected to Dirichlet‐mixed conditions. …”
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Heat transfer study of convective fin with temperature-dependent internal heat generation by hybrid block method by Alkasassbeh, Mohammad, Omar, Zurni, Mebarek-Oudina, Fateh, Raza, Jawad, Chamkha, Ali

“…Purpose: In this study, an implicit one‐step hybrid block method using two off‐step points involving the presence of a third derivative for solving second‐order boundary value problems are subjected to Dirichlet‐mixed conditions. …”
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Stagnation-point flow over a permeable stretching/shrinking sheet in a copper-water nanofluid by Bachok @ Lati, Norfifah, Ishak, Anuar, Nazar, Roslinda, Senu, Norazak

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A SOR solution of one-dimensional telegraph equations by using newly established Redlich-Kister finite difference schemes by Mohd Norfadli Suardi, Jumat Sulaiman

“…Various finite difference schemes have been established to discretize boundary value problems. Therefore, this paper proposes a numerical solution based on newly established second-order Redlich-Kister Finite Difference (RKFD) discretization schemes to approximate the one-dimensional second-order linear hyperbolic telegraph equation. …”
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Mathematical analysis of magnetohydrodynamic (MHD) flow of micropolar nanofluid under buoyancy effects past a vertical shrinking surface: dual solutions by Lund, Liaquat Ali, Omar, Zurni, Khan, Ilyas

“…The governing fluid flow equations of this problem are transformed into nonlinear boundary value problems (BVPs) of ordinary differential equations (ODEs) by applying similarity variables. …”
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Steady incompressible magnetohydrodynamics Casson boundary layer flow past a permeable vertical and exponentially shrinking sheet: A stability analysis by Lund, Liaquat Ali, Omar, Zurni, Khan, Ilyas

“…The resultant equations of boundary value problems are then converted into the equivalent initial value problems using the shooting method before they can be solved using Runge‐Kutta of order four. …”

Frozen Jacobian Multistep Iterative Method for Solving Nonlinear IVPs and BVPs by Ahmad, F., Rehman, S.U., Ullah, M.Z., Aljahdali, H.M., Ahmad, S., Alshomrani, A.S., Carrasco, J.A., Ahmad, S., Sivasankaran, S.

“…In this paper, we present and illustrate a frozen Jacobian multistep iterative method to solve systems of nonlinear equations associated with initial value problems (IVPs) and boundary value problems (BVPs). We have used Jacobi-Gauss-Lobatto collocation (J-GL-C) methods to discretize the IVPs and BVPs. …”

Complex variable solution of elastic tunneling problems by Fattah, M.Y., Hamoud, M.J., Salman, F.A., Raheem, A.H.A.

“…For this purpose, two elementary boundary value problems were considered in detail. These include the problem of a half plane with a circular cavity loaded by a uniform radial stress, and the problem in which a uniform radial displacement is imposed on the cavity boundary (this is usually called the ground loss problem). …”

An Improved Symmetric Numerical Approach for Systems of Second-Order Two-Point BVPs by Busyra Latif, Md Yushalify Misro, Samsul Ariffin Abdul Karim, Ishak Hashim

“…This study deals with the numerical solution of a class of linear systems of second-order boundary value problems (BVPs) using a new symmetric cubic B-spline method (NCBM). …”
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An effective wavelet neural network approach for solving first and second order ordinary differential equations by Lee Sen Tan, Lee Sen Tan, Zainuddin, Zarita, Pauline Ong, Pauline Ong, Abdullah, Farah Aini A

“…The proposed WNNs approach is then rigorously evaluated by solving first and second order ODEs, including initial value problems, singularly perturbed boundary value problems, and a Lane–Emden type equation. Comparative analyses against alternative training methods, other existing ANNs, and numerical techniques demonstrate the superior performance of the proposed method, affirming its efficiency and accuracy in approximating ODE solutions.…”
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Triple local similarity solutions of Darcy-Forchheimer Magnetohydrodynamic (MHD) flow of micropolar nanofluid over an exponential shrinking surface: stability analysis by Ali Lund, Liaquat, Ching, Dennis Ling Chua, Omar, Zurni, Khan, Ilyas, Nisar, Kottakkaran Sooppy

“…The resultant ODEs of the boundary value problems (BVPs) are renewed into initial value problems (IVPs) using a shooting method, and then the IVPs are solved by a fourth order Runge-Kutta (RK) method. …”
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A newton-modified weighted arithmetic mean solution of nonlinear porous medium type equations by Elayaraja Aruchunan, Chew, Jackel Vui Lung, Mohana Sundaram Muthuvalu, Andang Sunarto, Jumat Sulaiman

“…Some initial-boundary value problems with a different type of nonlinear diffusion term are presented. …”
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Effect of double stratification on boundary layer flow and heat of nanofluid over a vertical plate in the presence of chemical reaction by Rahamat, Lily Afizah

“…This software uses a fourth-fifth order Runge Kutta Fehlberg method as a default to solve boundary values problems numerically using the dsolve command. …”
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Effects of stefan blowing and slip conditions on unsteady MHD casson nanofluid flow over an unsteady shrinking sheet: Dual solutions by Lund, Liaquat Ali, Omar, Zurni, Raza, Jawad, Khan, Ilyas, Sherif, El-Sayed M.

“…The modeled equations of partial differential equations (PDEs) are transformed into the equivalent boundary value problems (BVPs) of ordinary differential equations (ODEs) by employing similarity transformations. …”
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Application Of The Differential Quadrature Method To Problems In Engineering Mechanics by Fakir, Md.Moslemuddin

“…The initial and/or boundary value problems can be solved by this method directly and efficiently. …”
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Finite element modelling of limiting dome high sheet metal formability test by Mohammad Amir, Hashim

“…The finite element method (FEM) is a computational technique used to obtain approximate solution of boundary value problems in engineering. The effect of dimension -in doing the analysis in Finete Element Modelling is important to make sure the analysis is completely rigth will analyze. …”
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The numerical approximation for the indentation of granular materials by a smooth rigid wedge punch by Syafikah, Ayob

“…The construction of the deformation region is the combination of boundary value problems formed by the network of the α− and β− characteristic lines. …”
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