Parallel Simulation of HGMS of Weakly Magnetic Nanoparticles in Irrotational Flow of Inviscid Fluid by Kanok Hournkumnuard, Banpot Dolwithayakul, Chantana Chantrapornchai

“…The differential equations governing particle transport are solved numerically as an initial and boundary values problem by using the finite-difference method. …”
Get full text

Generating Solar Sail Trajectories in the Earth-Moon System Using Augmented Finite-Difference Methods by Geoffrey G. Wawrzyniak, Kathleen C. Howell

“…Numerical techniques to solve boundary value problems can be employed to understand this challenging dynamical regime. …”
Get full text

Nonlinear Dynamic Analysis of Plates Stiffened by Parallel Beams with Deformable Connection by J. A. Dourakopoulos, E. J. Sapountzakis

“…These tractions are integrated with respect to each half of the interface width resulting in two interface lines, along which the loading of the beams and the additional loading of the plate are defined. Six boundary value problems are formulated and solved using the analog equation method (AEM), a BEM-based method. …”
Get full text

On numerical methods for time-dependent eddy current problems for the Maxwell equations in inhomogeneous media by A.A. Arbuzov, R.Z. Dautov, E.M. Karchevskii, M.M. Karchevskii, D.V. Chistyakov

“…The concept of generalized solutions for boundary-value problems in bounded regions for obtained systems of equations has been formulated. …”
Get full text

Noniterative Localized and Space-Time Localized RBF Meshless Method to Solve the Ill-Posed and Inverse Problem by Mohammed Hamaidi, Ahmed Naji, Fatima Ghafrani, Mostafa Jourhmane

“…In many references, both the ill-posed and inverse boundary value problems are solved iteratively. The iterative procedures are based on firstly converting the problem into a well-posed one by assuming the missing boundary values. …”
Get full text

Frozen Jacobian Multistep Iterative Method for Solving Nonlinear IVPs and BVPs by Fayyaz Ahmad, Shafiq Ur Rehman, Malik Zaka Ullah, Hani Moaiteq Aljahdali, Shahid Ahmad, Ali Saleh Alshomrani, Juan A. Carrasco, Shamshad Ahmad, Sivanandam Sivasankaran

“…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. …”
Get full text

Variable-Time-Domain Online Neighboring Optimal Trajectory Modification for Hypersonic Interceptors by Ningbo Li, Humin Lei, Jin Zhou, Lei Shao, Bin Wang

“…A trajectory optimization model is designed according to the features of operations in near space. Two-point boundary value problems (TPBVPs) are obtained based on NOC theory. …”
Get full text

APPROXIMATELY SINGULAR WAVELET by V. M. Romanchak

“…The universal algorithm of approximation makes it possible to apply it to approximate one-dimensional and multidimensional functions, in decision support systems, in the processing of stochastic information, pattern recognition, and solution of boundary-value problems.The introduction explain the idea of the method of singular wavelets – to combine the theory of wavelets with the Nadaraya-Watson kernel regression estimator. …”
Get full text

Exploration of Unsteady Squeezing Flow through Least Squares Homotopy Perturbation Method by Mubashir Qayyum, Imbsat Oscar

“…The least squares homotopy perturbation method (LSHPM) has been proposed to determine the solutions of nonlinear boundary value problems. To check the validity and convergence of the proposed scheme (LSHPM), the modeled problems are also solved with the Fehlberg–Runge–Kutta method (RKF45) and homotopy perturbation method (HPM) and residual errors are compared with LSHPM. …”
Get full text

Influence of Surface Energy Effects on Elastic Fields of a Layered Elastic Medium under Surface Loading by Supakorn Tirapat, Teerapong Senjuntichai, Jaroon Rungamornrat

“…This paper presents the analysis of a layered elastic half space under the action of axisymmetric surface loading and the influence of the surface energy effects. The boundary value problems for the bulk and the surface are formulated based on classical linear elasticity and a complete Gurtin-Murdoch constitutive relation. …”
Get full text

Exploring the Novel Continuum-Cancellation Leal-Method for the Approximate Solution of Nonlinear Differential Equations by Hector Vazquez-Leal

“…Furthermore, we present the application of CCLM in several examples: Thomas–Fermi singular equation for the neutral atom, magnetohydrodynamic flow of blood in a porous channel singular boundary-valued problem, and a system of initial condition differential equations to model the dynamics of cocaine consumption in Spain. …”
Get full text

A Multiregion Discrete-Time Epidemic Model of Mycobacterium tuberculosis Infections: An Optimal Control Approach by Rachid Bouajaji, Hassan Laarabi, Mostafa Rachik, Abdelhadi Abta

“…The numerical results associated with the multipoint boundary value problems are obtained based on the forward-backward sweep method combined with progressive-regressive Runge–Kutta fourth-order schemes.…”
Get full text

Micromechanics of Cracked Laminates under Uniaxial Load: A Comparison between Approaches by J. A. Rivera-Santana, A. Guevara-Morales, U. Figueroa-López

“…Afterwards, these boundary value problems (BVP) are solved in order to obtain a stress function which couples the initial and perturbation stresses, the latter being in function of crack density, thus related to material stiffness reduction. …”
Get full text

Two-phase Agrawal hybrid nanofluid flow for thermal and solutal transport fluxes induced by a permeable stretching/shrinking disk by Hatem Gasmi, Muhammad Waqas, Umair Khan, Aurang Zaib, Anuar Ishak, Imtiaz Khan, Ali Elrashidi, Mohammed Zakarya

“…Subsequently, these simplified equations achieved numerical solutions by employing the bvp4c solver, which is specifically designed for fourth-ordered boundary value problems. The study delves into the remarkable impacts of the pertinent embedded parameters on key parameters such as mass transfer rate, heat transfer rate, and shear stress. …”
Get full text

Ciliary peristalsis flow of hydromagnetic Sutterby nanofluid through symmetric channel: Viscous dissipation in case of variable electrical conductivity by Sameh A. Hussein, Sameh E. Ahmed, Anas A.M. Arafa

“…The problem-solving strategy depends on first transforming the system into a dimensionless form, after which using the lubrication approximation, the evolving boundary value problems has been normalized and linearized form. …”
Get full text

A Study of the Occurrence of Resonance under the Influence of Dynamic Forces on the Structural Elements of Electrical Installations by Y. V. Potachits

“…To solve these problems, mathematical models are compiled and boundary value problems are formulated for calculating the electrodynamic stability of structural elements, taking into account the possible coincidence of the frequencies of natural and forced oscillations of structural elements taking into account the probable coincidence of the frequencies of forced and natural vibrations of structural elements.…”
Get full text

Study results of the stress-strain states of the crown parts of molars restored with composite, ceramic and zirconium onlays by Y.A. Sardykov, M.H. Kryshchuk, O.O. Fastovets, R.Y. Matvieienko

“…The stress values were calculated using the method of linear scaling of the results of the numerical solution of the boundary value problems of the theory of elasticity for small deformations to correspond to the functional force load of the mandibular molar of 100 N. …”
Get full text

The Existence and Uniqueness of Nonlinear Elliptic Equations with General Growth in the Gradient by Angelo Alvino, Vincenzo Ferone, Anna Mercaldo

“…In this paper, we prove the existence and uniqueness results for a weak solution to a class of Dirichlet boundary value problems whose prototype is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><msub><mo>Δ</mo><mi>p</mi></msub><mi>u</mi><mo>=</mo><mi>β</mi><msup><mrow><mo>|</mo><mo>∇</mo><mi>u</mi><mo>|</mo></mrow><mi>q</mi></msup><mo>+</mo><mi>f</mi><mo> </mo><mrow><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo> </mo><mo>Ω</mo></mrow><mspace width="0.166667em"></mspace><mo>,</mo><mo> </mo><mi>u</mi><mo>=</mo><mn>0</mn><mo> </mo><mrow><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi><mo> </mo><mo>∂</mo><mo>Ω</mo></mrow><mspace width="0.166667em"></mspace><mo>,</mo><mspace width="4pt"></mspace></mrow></semantics></math></inline-formula> where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Ω</mo></semantics></math></inline-formula> is a bounded open subset of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mi>N</mi></msup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>≥</mo><mn>2</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo><</mo><mi>p</mi><mo><</mo><mi>N</mi></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mo>Δ</mo><mi>p</mi></msub><mi>u</mi><mo>=</mo><mi>div</mi><mfenced separators="" open="(" close=")"><msup><mrow><mo>|</mo><mo>∇</mo><mi>u</mi><mo>|</mo></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mo>∇</mo><mi>u</mi></mfenced></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>−</mo><mn>1</mn><mo><</mo><mi>q</mi><mo><</mo><mi>p</mi></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> is a positive constant and <i>f</i> is a measurable function satisfying suitable summability conditions depending on <i>q</i> and a smallness condition.…”
Get full text