A Method of Finding Source Function for Inverse Diffusion Problem with Time-Fractional Derivative by Vildan Gülkaç

“…The Homotopy Perturbation Method is developed to find a source function for inverse diffusion problem with time-fractional derivative. …”
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SOLUTION OF AN INVERSE PARABOLIC PROBLEM WITH UNKNOWN SOURCE-FUNCTION AND NONCONSTANT DIFFUSIVITY VIA THE INTEGRAL EQUATION METHODS

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Numerical Bichromatic Wave Generation Using Designed Mass Source Function by Min-yi Chen, Hong-sheng Zhang, En-xian Zhou, Da-li Xu

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On the Inverse Problem of the Fractional Heat-Like Partial Differential Equations: Determination of the Source Function by Gülcan Özkum, Ali Demir, Sertaç Erman, Esra Korkmaz, Berrak Özgür

“…The study in this paper mainly concerns the inverse problem of determining an unknown source function in the linear fractional differential equation with variable coefficient using Adomian decomposition method (ADM). …”
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On the source problem for the diffusion equations with conformable derivative by Van Anh Nghiem Thi, Anh Tuan Vu, Dinh Long Le, Vuong Nguyen Doan

“…In this article, we are interested in the problem of finding the source function of the diffusions equations \(\partial_{t}^\alpha - \Delta u =  f(x)\) (where \(f\) as the unknown source function and \(\alpha\in (0,1)\)). …”
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Optical Cryptanalysis Method Using Wavefront Shaping by Meihua Liao, Dajiang Lu, Wenqi He, Xiang Peng

“…In this paper, a practical optical cryptanalysis method using wavefront shaping is proposed. Considering that the confusion and diffusion of information in the optical cryptosystem are actually caused by scattering effect of random phase mask(s), the proposed method employs a point source function and the feedback-based optimization algorithm, which can obtain an equivalent key of the optical cryptosystem. …”
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Thermal Properties of Short Fibre Composites Modeled by Meshless Method by Vladimír Kompiš, Zuzana Murčinková

“…The developed method of continuous source functions is a boundary meshless method reducing the problem considerably comparing to other methods like FEM, BEM, meshless methods, or fast multipole BEM formulation.…”
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Extension of the First-Order Recursive Filters Method to Non-Linear Second-Kind Volterra Integral Equations by Rodolphe Heyd

“…Unlike most numerical methods based on the Laplace transformation, the IIRFM-A method has the dual advantage of requiring neither the calculation of the Laplace transform of the source function nor that of intermediate inverse Laplace transforms. …”
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Analysis Method for the Pouring Stage of Concrete-Filled Steel Tube (CFST) Arch Bridges Considering Time-Varying Heat of Hydration and Elastic Modulus by Mengsheng Yu, Xinyu Yao, Kaizhong Xie, Tianzhi Hao, Xirui Wang

“…Firstly, based on the composite index model of the hydration heat and through the reduction of the participating materials, the heat source function of the hydration heat of the arch rib was obtained, and its accuracy was verified by using two test components. …”
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On the stable approximate solution of the ill-posed boundary value problem for the Laplace equation with homogeneous conditions of the second kind on the edges at inaccurate data o... by Evgeniy B. Laneev, Alexander V. Klimishin

“…On the basis of an idea about the source function of the original problem, the exact solution is represented as a sum of two functions, one of which depends explicitly on the Cauchy conditions, and the second one can be obtained as a solution of the Fredholm integral equation of the first kind in the form of Fourier series on the eigenfunctions of the second boundary value problem for the Laplace equation. …”
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Inverse Source Problem for a Multiterm Time-Fractional Diffusion Equation with Nonhomogeneous Boundary Condition by L. L. Sun, X. B. Yan

“…The inverse problem is solved by the Levenberg-Marquardt regularization method, and an approximate source function is found. …”
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Modelling the Formation and Propagation of Nonlinear Waves in Dynamical Systems with Sources by Meirim Amantay, Arnold Brener, Madina Balabekova, Kamil Kayumov, Akhmet Musabekov

“…The main objective of this paper is to develop a fairly general mathematical model allowing for identifying a set of parameters for controlling the propagation of nonlinear wave processes in dynamic systems with sources without specifying an explicit form of the source function. To solve the problem, the paper develops approaches based on the adaptation of methods for deriving the perturbed Korteweg-de-Vries equation taking into account the nonlocality of the response based on the Whitham integro-differential equation. …”
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Investigation on the Radar Scattering and Doppler Spectrum From Trimaran Based on the Motion of Six Degrees of Freedom by Yuxin Deng, Jinxing Li, Wangqiang Jiang, Min Zhang

“…Second, an accelerated geometrical optics and physical optics algorithm using the light source function (GO-PO/LSF) is proposed, which uses the light source function to realize the visibility judgment of surfaces and greatly reduces the computation time. …”
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The carbon source-sink function of Hulun Lake, a large shallow eutrophic lake in northern China by Fengju Zhang, Bin Xue, Shuchun Yao

“…While further research is necessary to generalize these findings, our results provide compelling evidence for the significant role of lakes in the carbon cycle, and highlighting the importance of considering both carbon burial and carbon emission in assessments of the carbon sink-source function.…”
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The Existence of Solution of Diffusion Equation with the General Conformable Derivative by Shanshan Li, Shuqin Zhang, Ruiying Liu

“…By the maximum principle, this paper proves the uniqueness of the solution and the continuous dependence on source function and initial-boundary conditions of the solution. …”
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Realizing depth measurement and edge detection based on a single metasurface by Yang Siwen, Wei Qunshuo, Zhao Ruizhe, Li Xin, Zhang Xue, Li Yao, Li Junjie, Jing Xiaoli, Li Xiaowei, Wang Yongtian, Huang Lingling

“…Double helix point source function is utilized, and three verification experiments are carried out, including double-helix beam calibration, 2D object and 3D object detection, respectively. …”
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Increasing Stability in the Inverse Source Problem with an Interval (<i>K</i>₁, <i>K</i>₂) of Frequencies by Suliang Si

“…The method is based on the Fourier transform and explicit bounds for analytic continuation.…”
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Production Decline Analysis for Two-Phase Flow in Multifractured Horizontal Well in Shale Gas Reservoirs by Wei-Yang Xie, Xiao-Ping Li, Lie-Hui Zhang, Xiao-Hua Tan, Jun-Chao Wang, Hai-Tao Wang

“…Accurate solution to this flow model is obtained by the use of source function theory, Laplace transform, three-dimensional eigenvalue method, and orthogonal transformation. …”
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INTEGRAL TRANSFORMATION IN A PARTIALLY BOUNDED REGION WITH A RADIAL THERMAL FLOW by E. M. Kartashov

“…At the same time, for the above-mentioned region, the method of Green's functions was developed by constructing integral representations of analytical solutions of the first, second and third boundary value problems through inhomogeneities in the initial formulation of the problem (boundary conditions, source function in the initial equation). …”
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A Semianalytical Model for Simulating Fluid Flow in Tight Sandstone Reservoirs with a Bottom Aquifer by Suran Wang, Yuhu Bai, Bingxiang Xu, Ling Chen, Wenlan Li, Yanzun Li

“…In the model, the hydraulic fracture is handled discretely with a numerical discrete method. The three-dimensional volumetric source function in real space and superposition principle are employed to solve the model analytically for fluid flow in the reservoir. …”
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