Results 1 to 10 of about 1,675 (248)
First-Order Singular and Discontinuous Differential Equations
Boundary Value Problems, 2009 We use subfunctions and superfunctions to derive sufficient conditions for the existence of extremal solutions to initial value problems for ordinary differential equations with discontinuous and singular nonlinearities.
Daniel C. Biles +1 more
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Local discontinuous Galerkin methods for fractional ordinary differential equations [PDF]
BIT Numerical Mathematics, 2014 This paper discusses the upwinded local discontinuous Galerkin methods for the one-term/multi-term fractional ordinary differential equations (FODEs). The natural upwind choice of the numerical fluxes for the initial value problem for FODEs ensures stability of the methods.
Jan Hesthaven +2 more
exaly +4 more sources
Upper and Lower Solutions for First-Order Discontinuous Ordinary Differential Equations
Journal of Mathematical Analysis and Applications, 2000 The paper contains a significant contribution to the classical method of upper and lower solutions for a nonlinear first-order differential equation \(x'(t)=f(t,x(t)), t\in I=[0,1]\), with \(f:I\times \mathbb{R}\to \mathbb{R}\). The author generalizes the previous results in several directions: 1.
Rodrigo López-Pouso
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Solving Ordinary Differential Equations with Discontinuities [PDF]
ACM Transactions on Mathematical Software, 1984 Automatic codes for differential equations can be inadequate when the solutions have discontinuities. If the user provides an external indicator for discontinuities (e.g., a switching function whose sign changes indicate discontinuities), a code can be more efficient.
Gear, C. W., Østerby, Ole
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Lyapunov Instability for Discontinuous Differential Equations
Intermaths, 2021 The present work studies the Lyapunov instability for discontinuous differential equations through the use of the notion of Carathéodory solution to differential equations.
Iguer Luis Domini dos Santos
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Axioms, 2023 For the purpose of solving elliptic partial differential equations, we suggest a new approach using an h-adaptive local discontinuous Galerkin approximation based on Sinc points.
Omar A. Khalil, Gerd Baumann
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Ratio Mathematica, 2023 A linear system of ’n’ second order ordinary differential equations of reaction-diffusion type with discontinuous source terms is considered. On a piecewise uniform Shishkin mesh, a numerical system is built that employs the finite element method.
Vinoth Maruthamuthu +1 more
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Discontinuous Galerkin methods for ordinary differential equations [PDF]
Mathematics of Computation, 1981 A class of Galerkin methods derived from discontinuous piecewise polynomial spaces is analyzed. For polynomials of degree k , these methods lead to a family of one-step schemes generating approximations up to order
Delfour, M., Hager, W., Trochu, F.
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Comptes Rendus. Mathématique, 2023 We study nonlocal conservation laws with a discontinuous flux function of regularity $\mathsf {L}^{\infty }(\mathbb{R})$ in the spatial variable and show existence and uniqueness of weak solutions in $\mathsf {C}\big ([0,T]; \mathsf {L}^{1}_{\mathrm{loc}}
Keimer, Alexander, Pflug, Lukas
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Boundary Value Problems, 2009 We present some new nonlinear integral inequalities Bellman-Bihari type with delay for discontinuous functions (integro-sum inequalities; impulse integral inequalities). Some applications of the results are included: conditions of boundedness (uniformly),
Angela Gallo, Anna Maria Piccirillo
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