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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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Modification of Chebyshev Pseudospectral Method to Minimize the Gibbs Oscillatory Behaviour in Resynthesizing Process
The Gibbs phenomenon describes oscillations of small or large amplitudes that occur, when a signal with steep gradients or noise components is...
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Use of the Chebyshev Collocation Method for Vibration Analysis of Carbon-Nanotube Reinforced Composite Beams with Elastic Boundary Conditions
An investigation of the vibration behaviour of carbon-nanotube reinforced composite beams utilizing both traditional and non-traditional boundary...
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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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Application of a Chebyshev Collocation Method to Solve a Parabolic Equation Model of Underwater Acoustic Propagation
The parabolic approximation has been used extensively for underwater acoustic propagation and is attractive because it is computationally efficient....
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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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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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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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A bivariate Chebyshev polynomials method for nonlinear dynamic systems with interval uncertainties
A bivariate Chebyshev polynomials approach is proposed to estimate the dynamic response bounds of nonlinear systems with interval uncertainties. The...
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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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A novel Chebyshev-Gauss pseudospectral method for accurate milling stability prediction
As a major limitation on the process efficiency of the manufacturing industry, milling chatter can be effectively alleviated by the optimal parameter...
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Parallel Evaluation of Chebyshev Approximations: Applications in Astrodynamics
Approximations based on Chebyshev polynomials have several astrodynamic applications. The performance of these approximations can be improved by...
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Chebyshev Spectral Projection Methods for Fredholm Integral Equations of the Second Kind
In this paper, we will propose the Chebyshev spectral Galerkin and collocation methods for the Fredholm integral equations (fies) of the second kind...
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Numerical solutions for distributed-order fractional optimal control problems by using generalized fractional-order Chebyshev wavelets
This paper studies a numerical approach based on generalized fractional-order Chebyshev wavelets for solving distributed-order fractional optimal...
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Dynamic response of bidirectional functionally graded beams with elastic supports and foundations under moving harmonic loads
Dynamic behavior of elastically supported bidirectional functionally graded (BDFG) beams resting on an elastic foundation under a moving harmonic...
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An Adaptive Local Variational Iteration Method for Orbit Propagation in Astrodynamics Problems
In this paper, a highly accurate and efficient Adaptive Local Variational Iteration Method (ALVIM) is presented to fulfil the need of the...
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Numerical solutions of Schrödinger wave equation and Transport equation through Sinc collocation method
This study carries the novel applications of the Sinc collocation method to investigate the numerical computing paradigm of Schrödinger wave equation...
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Application of Bernstein Collocation Solutions for Solving Second Kind Volterra–Fredholm Integral Equations
Single and multiple integral problemsMultiple integral problems are often applied in pure analysis, mechanical vibration, and related engineering and...
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Probabilistic Response and Short-Term Extreme Load Estimation of Offshore Monopile Wind Turbine Towers by Probability Density Evolution Method
A new analysis framework based on probability density evolution method (PDEM) and its Chebyshev collocation solution are introduced to predict the...
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Hamilton–Pontryagin spectral-collocation methods for the orbit propagation
According to the discrete Hamilton–Pontryagin variational principle, we construct a class of variational integrators in the real vector spaces and...
