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Collocation Method for Solving Two-Dimensional Fractional Volterra Integro-Differential Equations
In this paper, the collocation method is extended for solving two-dimensional fractional Volterra integro-differential equations (2D-FVIDEs). First,...
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A Lagrange spectral collocation method for weakly singular fuzzy fractional Volterra integro-differential equations
A linear fractional-order weakly singular fuzzy Volterra integro-differential equation has been examined. In this case, the Caputo fractional-order...
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Nonlinear Model Predictive Path Tracking Control for Autonomous Vehicles Based on Orthogonal Collocation Method
Autonomous vehicles have gained popularity over the past few years. In this paper, we present a nonlinear model predictive control approach for...
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Space–time collocation meshfree method for modeling 3D wave propagation problems
In this work, a novel local space–time domain collocation technique—space–time boundary moving least squares (BMLS–ST) method, which has been...
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Collocation methods for second and higher order systems
It is often unnoticed that the predominant way to use collocation methods is fundamentally flawed when applied to optimal control in robotics. Such...
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Numerical Solution of Nonlinear Reaction-Advection-Diffusion Equation in Sense of Caputo-Fabrizio Derivative with Finite Difference and Collocation Method
In this paper, we consider a nonlinear reaction-diffusion equation with a Caputo-Fabrizio derivative and its solution is obtained by the finite...
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A spectral shifted gegenbauer collocation method for fractional pantograph partial differential equations and its error analysis
This study presents a new numerical approach for solving fractional-order pantograph partial-differential equations, in which the fractional...
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Localized collocation schemes and their applications
This paper presents a summary of various localized collocation schemes and their engineering applications. The basic concepts of localized...
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Analysis of multiple parallel cracks in a functionally graded magneto-electro-elastic plane using boundary collocation method
The fracture behavior of a functionally graded magneto-elastic plane with multiple parallel cracks is examined in this article. Under anti-plane...
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Enhancing PINNs for solving PDEs via adaptive collocation point movement and adaptive loss weighting
Physics-informed neural networks (PINNs) are an emerging method for solving partial differential equations (PDEs) and have been widely applied in the...
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Consistency, precision, and accuracy assessment of the collocation boundary element method for two-dimensional problems of potential and elasticity
The collocation boundary element method, as developed and taught in the traditional books, suffers from severe inconsistencies, partly responsible...
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An adaptive wavelet-based collocation method for solving multiscale problems in continuum mechanics
Computational multiscale methods are highly sophisticated numerical approaches to predict the constitutive response of heterogeneous materials from...
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A sixth-order wavelet integral collocation method for solving nonlinear boundary value problems in three dimensions
A sixth-order accurate wavelet integral collocation method is proposed for solving high-order nonlinear boundary value problems in three dimensions....
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Multi-resolution Trajectory Optimization of eVTOL Aircraft Using Capacity Collocation
Electric vertical takeoff and landing (eVTOL) aircraft has advantages of cleaner, quieter, and more comfortable flight over its conventional...
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A Strong Form Meshfree Collocation Method: Engineering Applications Including Frictional Contact
This article provides the brief review of the recently developed strong form meshfree collocation method. The method directly discretizes a strong...
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A least squares recursive gradient meshfree collocation method for superconvergent structural vibration analysis
A least squares recursive gradient meshfree collocation method is proposed for the superconvergent computation of structural vibration frequencies....
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Two and Three-Dimensional Computation of Dispersion Curves of Ultrasonic Guided Waves in Isotropic Plates by the Spectral Collocation Method
The field of non-destructive evaluations (NDE) using ultrasonic waves is widely used in industry to guarantee the safety and proper functioning of...
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On Mixed Steps-Collocation Schemes for Nonlinear Fractional Delay Differential Equations
This research deals with the numerical solution of fractional differential equations with delay using the method of steps and shifted Legendre...
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Solution to boundary value problems on linear elastic confocal elliptic domain based on collocation technique
Domains with elliptic boundaries are regularly pursued in Elasticity to elucidate the role of circular asymmetry and are associated with many...
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A novel collocation beam element based on absolute nodal coordinate formulation
The computational efficiency has been largely hindering the application of the absolute nodal coordinate formulation (ANCF). To improve the...
