An approximation method for the solution of nonlinear integral equations [PDF]
, 2006 A Chebyshev collocation method has been presented to solve nonlinear integral equations in terms of Chebyshev polynomials. This method transforms the integral equation to a matrix equation which corresponds to a system of nonlinear algebraic equations ...
Akyuz-Dascioglu, A, Yaslan, HC
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A novel integral transform operator and its applications [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2023 The proposed study is focused to introduce a novel integral transform op-erator, called Generalized Bivariate (GB) transform. The proposed trans-form includes the features of the recently introduced Shehu transform, ARA transform, and Formable transform.
Sh. Arora, A. Pasrija
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Application of wavelets to singular integral scattering equations [PDF]
, 2004 The use of orthonormal wavelet basis functions for solving singular integral scattering equations is investigated. It is shown that these basis functions lead to sparse matrix equations which can be solved by iterative techniques.
B. M. Kessler +10 more
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High-order, Dispersionless "Fast-Hybrid" Wave Equation Solver. Part I: $\mathcal{O}(1)$ Sampling Cost via Incident-Field Windowing and Recentering [PDF]
, 2020 This paper proposes a frequency/time hybrid integral-equation method for the time dependent wave equation in two and three-dimensional spatial domains.
Anderson, Thomas G. +2 more
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Linear integral equations, infinite matrices, and soliton hierarchies [PDF]
Journal of Mathematics and Physics, 2017 A systematic framework is presented for the construction of hierarchies of soliton equations. This is realised by considering scalar linear integral equations and their representations in terms of infinite matrices, which give rise to all (2+1)- and (1+1)
Wei-jie Fu, F. Nijhoff
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Beyond Laplace and Fourier transforms: Challenges and future prospects
Thermal Science, 2023 Laplace and Fourier transforms are widely used independently in engineering for linear differential equations including fractional differential equations.
JI-HUAN He +3 more
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Bäcklund transformations for integrable lattice equations [PDF]
Journal of Physics A: Mathematical and Theoretical, 2008 We give new Backlund transformations (BTs) for some known integrable (in the sense of being multidimensionally consistent) quadrilateral lattice equations. As opposed to the natural auto-BT inherent in every such equation, these BTs are of two other kinds. Specifically, it is found that some equations admit additional auto-BTs (with Backlund parameter),
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Multicomponent integrable wave equations: I. Darboux-dressing transformation [PDF]
Journal of Physics A: Mathematical and Theoretical, 2007 The Darboux-Dressing Transformations are applied to the Lax pair associated to systems of coupled nonlinear wave equations in the case of boundary values which are appropriate to both bright and dark soliton solutions. The general formalism is set up and the relevant equations are explicitly solved. Several instances of multicomponent wave equations of
Degasperis, A., Lombardo, S.
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Fractional integral equations and state space transforms
Bernoulli, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
B. Buchmann, C. Klüppelberg
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A transition integral transform obtained from generalization of the Fourier transform
Ain Shams Engineering Journal, 2019 We introduce a generalized integral transform (GIT) whose integration path lies on the complex plane. The GIT has both bilateral and unilateral versions, and generalizes a set of known integral transforms, e.g. Fourier, Laplace, allowing to solve integro-
Rafael G. González-Acuña +1 more
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