Solving Hyperchaotic Systems Using the Spectral Relaxation Method by S. S. Motsa, P. G. Dlamini, M. Khumalo

“…A new multistage numerical method based on blending a Gauss-Siedel relaxation method and Chebyshev pseudospectral method, for solving complex dynamical systems exhibiting hyperchaotic behavior, is presented. …”
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Numerical Solutions of Fractional Integrodifferential Equations of Bratu Type by Using CAS Wavelets by Mingxu Yi, Kangwen Sun, Jun Huang, Lifeng Wang

“…A numerical method based on the CAS wavelets is presented for the fractional integrodifferential equations of Bratu type. …”
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Numerical Built-In Method for the Nonlinear JRC/JCS Model in Rock Joint by Qunyi Liu, Wanli Xing, Ying Li

“…Thereafter, the numerical implement method and implementation process of the JRC/JCS model were discussed and the reliability of the numerical method was verified by the shear tests of jointed rock mass. …”
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Free Transverse Vibration of Orthotropic Thin Trapezoidal Plate of Parabolically Varying Thickness Subjected to Linear Temperature Distribution by Arun Kumar Gupta, Shanu Sharma

“…The present paper deals with the free transverse vibration of orthotropic thin trapezoidal plate of parabolically varying thickness in x-direction subjected to linear temperature distribution in x-direction through a numerical method. The deflection function is defined by the product of the equations of the prescribed continuous piecewise boundary shape. …”
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Pathfinding for Mobile Robot Navigation by Exerting the Quarter-Sweep Modified Accelerated Overrelaxation (QSMAOR) Iterative Approach via the Laplacian Operator by A’qilah A. Dahalan, Azali Saudi, Jumat Sulaiman

“…Within this study, improving the navigation problem of a mobile robot iteratively by using a numerical method based on the potential field method is one of the main aims. …”
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A Novel Differential Evolution Invasive Weed Optimization Algorithm for Solving Nonlinear Equations Systems by Yongquan Zhou, Qifang Luo, Huan Chen

“…In view of the traditional numerical method to solve the nonlinear equations exist is sensitive to initial value and the higher accuracy of defects. …”
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Optimal trajectories in $L^1$ and under $L^1$ penalizations by Dumas, Annette, Santambrogio, Filippo

“…We then use modern algorithms in non-smooth convex optimization in order to obtain a numerical method to simulate such solutions.…”
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New Fractional Derivative Expression of the Shifted Third-Kind Chebyshev Polynomials: Application to a Type of Nonlinear Fractional Pantograph Differential Equations by Y. H. Youssri, W. M. Abd-Elhameed, H. M. Ahmed

“…To test the method’s convergence, certain estimations are included. The proposed numerical method is demonstrated by numerical results to ensure its applicability and efficiency.…”
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Free Vibration Analysis of Arbitrary-Shaped Plates Based on the Improved Rayleigh–Ritz Method by Wenjie Guo, Qingsong Feng

“…Adopting the spring model to simulate the general boundary conditions, the problems of vibration of the arbitrary plate domain can be solved perfectly. Then, a numerical method is introduced to figure out the structure strain energy, kinetic energy, and elastic potential energy of the boundary. …”
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Numerical High-Order Model for the Nonlinear Elastic Computation of Helical Structures by Fatima Boussaoui, Hassane Lahmam, Bouazza Braikat

“…In this work, we propose a high-order algorithm based on the asymptotic numerical method (ANM) for the nonlinear elastic computation of helical structures without neglecting any nonlinear term. …”
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Dynamic Analysis of Engine Bearings by H. Hirani, K. Athre, S. Biswas

“…The results obtained by present approximation are compared with those obtained by numerical method. The influence of thermal effects on the stiffness and damping coefficients is predicted by using a simplified thermal analysis. …”
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Study on the Technical Status of Old Concrete Truss-Arch Bridge Based on Vehicle-Bridge Interaction by Renchao Xie, Ming Li, Chihao Xu

“…It can be concluded that the proposed numerical method can be widely used to assess the technical state of the old concrete truss-arch bridges in poor condition.…”
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Numerical Simulation of a Class of Hyperchaotic System Using Barycentric Lagrange Interpolation Collocation Method by Xiaofei Zhou, Junmei Li, Yulan Wang, Wei Zhang

“…Based on this problem, this paper introduces another novel numerical method to solve a class of hyperchaotic system. …”
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High Precise Scattering Centers Models for Cone-Shaped Targets Based on Induced Currents by Qi-Feng Li, Kun-Yi Guo, Xin-Qing Sheng, Tian-Shu Liu

“…In order to validate the scattering center model, numerical simulations of two cone-shaped targets are presented, and the accuracies of the models are validated through comparing the range profiles simulated by the models with those by a full-wave numerical method. The validation results demonstrate that this model is superior to the existing model in precisely characterizing the scattering centers induced by creeping waves.…”
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Fitted Tension Spline Scheme for a Singularly Perturbed Parabolic Problem With Time Delay by Sisay Ketema Tesfaye, Gemechis File Duressa, Tekle Gemechu Dinka, Mesfin Mekuria Woldaregay

“…To overcome this drawback, a numerical method comprising the backward Euler scheme in the time direction and the fitted spline scheme in the space direction on uniform meshes is proposed. …”
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Numerical Approximation of Compressible Two-Phase Six-Equation Model Using CE/SE and RKDG Schemes by Omar Rabbani, Saqib Zia, Munshoor Ahmed, Asad Rehman, Ilyas Khan, Mulugeta Andualem

“…This scheme offers an effective numerical method for several continuum mechanics problems. …”
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The number of nonunimodular roots of a reciprocal polynomial by Stankov, Dragan

“…We present an algorithm for calculating the limit ratio and a numerical method for its approximation. We estimated the limit ratio for a family of polynomials deduced from the powers of a given Salem number. …”
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On a mathematical model of bone marrow metastatic niche by Ana Isabel Muñoz, J. Ignacio Tello

“…We also simulate the system to illustrate the qualitative behavior of the solutions. The numerical method of resolution is also presented in detail.…”
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Natural Frequency Analysis of Two Nonlinear Panels Coupled with a Cavity Using the Approximate Elliptic Integral Solution and the Method of Harmonic Residual Minimization by Y. Y. Lee

“…The results obtained from the proposed method approach are verified with those from a numerical method. The effects of vibration amplitude, gap width, aspect ratio, the numbers of acoustic modes and harmonic terms, and so forth on the resonant frequencies of the in-phase and out of phase modes are examined.…”
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Analytic Approximation of Solutions of Parabolic Partial Differential Equations with Variable Coefficients by Vladislav V. Kravchenko, Josafath A. Otero, Sergii M. Torba

“…In the paper, the Dirichlet boundary conditions are considered; however, the proposed method can be easily extended onto other standard boundary conditions. The proposed numerical method is shown to reveal good accuracy.…”
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