Approximate solution of stochastic Volterra integro-differential equations by using moving least squares scheme and spectral collocation method

In the traditional case, the uncertainty of the ambient temperature measured by the experiential distributed sensor is considered. In this paper, a model based on the moving least square method in the fusion algorithm is proposed to study the optimal monitoring point of the sensor in the greenhouse and determine the most suitable installation position of the sensor in the greenhouse to improve the control effect of the temperature control device of the system. MATLAB simulation software is used to simulate each working condition of the greenhouse. Temperature data measured at 15 locations in the greenhouse were used to evaluate all possible combinations of monitoring locations and to estimate the optimal location for indoor temperature sensors. Compared with the traditional method, the error is reduced to 0.373, and the data are more accurate.

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“…In the local region of a fitting function selected, the fitting function is [18][19][20][21][22][23]:…”

Section: Establishment Of Fitting Functionmentioning

confidence: 99%

Location Optimization Model of a Greenhouse Sensor Based on Multisource Data Fusion

Qiao

Zhang

Liu³

et al. 2022

Complexity

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“…In these methods, a finite expansion (with unknown coefficients) is considered as the solution of the problem, and by replacing it in the original equation, the expansion coefficients and consequently the solution of problem are obtained. Some of the recently used projection methods for such stochastic equations are Jacobi polynomials Galerkin method [24], cubic B‐spline method [28], moving least squares method [29], block‐pulse method [30], Bernstein polynomials method [31], and Legendre collocation method [32].…”

Section: Introductionmentioning

confidence: 99%

A projection method based on the piecewise Chebyshev cardinal functions for nonlinear stochastic ABC fractional integro‐differential equations

Heydari,

Zhagharian,

Cattani

2024

Math Methods in App Sciences

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In this study, the Atangana–Baleanu fractional derivative in the Caputo type (as a kind of non‐local and non‐singular derivative) is used to define a new class of stochastic fractional integro‐differential equations. A projection method (more precisely, a Galerkin approach) based on the piecewise Chebyshev cardinal functions is developed to solve these stochastic fractional equations. To construct this method, the operational matrices of fractional and stochastic integrals of these basis functions are obtained and used in the established method. By approximating the solution of the problem with a finite expansion of the expressed basis functions (in which the expansion coefficients are unknown), a system of algebraic equations is obtained. By solving this system, the expansion coefficients and subsequently the solution of the original stochastic fractional problem are obtained. The convergence analysis of the proposed method is investigated, theoretically and numerically. The accuracy of the established procedure is illustrated by solving several numerical examples.

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“…A single-step method for IDEs is given in [15]. The other numerical methods for different types of IDEs are the spectral collocation methods [16], Cubic B-spline approximation [17], collocation methods based on polynomials [18], and meshless methods [19].…”

Section: Introductionmentioning

confidence: 99%

A higher-order collocation method based on Haar wavelets for integro-differential equations with two-point integral condition

Ahsan,

Lei,

Alwuthaynani

et al. 2023

Phys. Scr.

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In this article, the higher-order Haar wavelet collocation method (HCMHW) is investigated to solve linear and nonlinear integro-differential equations (IDEs) with two types of conditions: simple initial condition and the point integral condition. We reproduce and compare the numerical results of the conventional Haar wavelet collocation method (CMHW) with those of HCMHW, demonstrating the superior performance of HCMHW across various conditions. Both methods effectively handle different types of given conditions. However, numerical results reveal that HCMHW exhibits a faster convergence rate than CMHW. To address nonlinear IDEs, we employ the quasi-linearization technique. The computational stability of both methods is evaluated through various experiments. Additionally, the article provides examples to illustrate the overall performance and accuracy of HCMHW compared to CMHW for both linear and nonlinear IDEs.

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Approximate solution of stochastic Volterra integro-differential equations by using moving least squares scheme and spectral collocation method

Cited by 19 publications

References 27 publications

Location Optimization Model of a Greenhouse Sensor Based on Multisource Data Fusion

Location Optimization Model of a Greenhouse Sensor Based on Multisource Data Fusion

A projection method based on the piecewise Chebyshev cardinal functions for nonlinear stochastic ABC fractional integro‐differential equations

A higher-order collocation method based on Haar wavelets for integro-differential equations with two-point integral condition

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