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Numerical integration of a nonlinear, singular integro-partial differential equation
Journal of Computational Physics, 1970Abstract A method for numerical integration of a nonlinear, singular integro-partial differential equation is presented. The method consists in evaluating the singular integral by a least-squares approximation technique. A predictor-corrector formula is employed to integrat- the ordinary differential equations obtained after the spatial ...
Prasad, K. Krishna, Hering, R. G.
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Mathematics and Computers in Simulation, 2023
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Sandip Maji, Srinivasan Natesan
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sandip Maji, Srinivasan Natesan
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Monotone methods and attractivity results for Volterra integro-partial differential equations
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1981SynopsisA Volterra integro-partial differential equation of parabolic type, which describes the time evolution of a population in a bounded habitat, subject both to past history and space diffusion effects, is investigated; general homogeneous boundary conditions are admissible.
SCHIAFFINO A, TESEI, Alberto
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Applied Mathematics and Computation, 2002
The authors derive asymptotic estimates for solutions to the Cauchy problem for the generic (``master'') partial integro-differential equation \[ \partial v(t, x)/\partial t= -w(t, x)v(t,x)+ \int_{v\in D} W(t; x| y) v(t,y)\,dy, \] where \(D\subset\mathbb{R}^2\) is bounded and Lebesgue measurable; the kernel \(W(t;x| y)\) describes the transition rate ...
Tabata, Minoru, Eshima, Nobuoki
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The authors derive asymptotic estimates for solutions to the Cauchy problem for the generic (``master'') partial integro-differential equation \[ \partial v(t, x)/\partial t= -w(t, x)v(t,x)+ \int_{v\in D} W(t; x| y) v(t,y)\,dy, \] where \(D\subset\mathbb{R}^2\) is bounded and Lebesgue measurable; the kernel \(W(t;x| y)\) describes the transition rate ...
Tabata, Minoru, Eshima, Nobuoki
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Domain decomposition methods for a class of integro-partial differential equations
AIP Conference Proceedings, 2016This paper deals with the construction of Schwarz Waveform Relaxation (SWR) methods for fractional diffusion-wave equations. SWR methods are a class of domain decomposition algorithms to solve evolution problems in parallel and have been mainly developed and analysed for several kinds of PDEs. We first analyse the convergence behaviour of the classical
CONTE, Dajana, CALIFANO, GIOVANNA
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Existence and asymptotic results for a system of integro-partial differential equations
Nonlinear Differential Equations and Applications NoDEA, 1996The paper is concerned with a non-Fourier phase field model of a solidification process expressed by an initial-boundary value problem for a system of integro-partial differential equations with delay. The authors prove the global existence and uniqueness of the solution and investigate the regularity and the asymptotic behavior of the solution as \(t ...
Aizicovici, Sergiu, Barbu, Viorel
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IEEE Transactions on Electromagnetic Compatibility, 2021
We derive the integro-partial differential equations with delay effect based on the Maxwell equations for a two-line system under the thin-wire approximation and the approximation of neglecting the interwire distance in the delay term. We introduce the normal- and common-mode and write the integro-partial differential equations in terms of these two ...
Shuji Kitora +3 more
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We derive the integro-partial differential equations with delay effect based on the Maxwell equations for a two-line system under the thin-wire approximation and the approximation of neglecting the interwire distance in the delay term. We introduce the normal- and common-mode and write the integro-partial differential equations in terms of these two ...
Shuji Kitora +3 more
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Energy Inequalities for Integro-Partial Differential Equations with Riemann–Liouville Integrals
SIAM Journal on Mathematical Analysis, 1992Integro-differential equations with Riemann-Liouville integrals are studied. These equations interpolate between the heat and the wave equation. The author derives energy inequalities. The proofs depend on Fourier analysis and probability methods.
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2010
In this paper, first the properties of one and two-dimensional differential transforms are presented.Next, by using the idea of differential transform, we will present a method to find an approximate solution fora Volterra integro-partial differential equations.
MOHSENI MOGHADAM, M., SAEEDI, H.
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In this paper, first the properties of one and two-dimensional differential transforms are presented.Next, by using the idea of differential transform, we will present a method to find an approximate solution fora Volterra integro-partial differential equations.
MOHSENI MOGHADAM, M., SAEEDI, H.
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An integro-partial differential equation for modeling biofluids flow in fractured biomaterials
Journal of Theoretical Biology, 2011A novel mathematical model in the framework of a nonlinear integro-partial differential equation governing biofluids flow in fractured biomaterials is proposed, solved, verified, and evaluated. A semi-analytical solution is derived for the equation, verified by a mass-lumped Galerkin finite element method (FEM), and calibrated with two in vitro ...
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