Search results for "Numerical partial differential equations"

showing 10 items of 27 documents

Multiplicity results for a class of asymmetric weakly coupled systems of second order ordinary differential equations

2005

We prove the existence and multiplicity of solutions to a two-point boundary value problem associated to a weakly coupled system of asymmetric second-order equations. Applying a classical change of variables, we transform the initial problem into an equivalent problem whose solutions can be characterized by their nodal properties. The proof is developed in the framework of the shooting methods and it is based on some estimates on the rotation numbers associated to each component of the solutions to the equivalent system.

Algebra and Number TheoryMathematical analysislcsh:QA299.6-433lcsh:AnalysisExponential integratorStochastic partial differential equationLinear differential equationCollocation methodOrdinary differential equationmultiplicity result asymmetric weakly coupled system nodal solutions rotation numberBoundary value problemAnalysisMathematicsSeparable partial differential equationNumerical partial differential equations
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Fixed point theorems for fuzzy mappings and applications to ordinary fuzzy differential equations

2014

Abstract Ran and Reurings (Proc. Am. Math. Soc. 132(5):1435-1443, 2004) proved an analog of the Banach contraction principle in metric spaces endowed with a partial order and discussed some applications to matrix equations. The main novelty in the paper of Ran and Reurings involved combining the ideas in the contraction principle with those in the monotone iterative technique. Motivated by this, we present some common fixed point results for a pair of fuzzy mappings satisfying an almost generalized contractive condition in partially ordered complete metric spaces. Also we give some examples and an application to illustrate our results. MSC:46S40, 47H10, 34A70, 54E50.

Algebra and Number Theoryfuzzy mappingApplied MathematicsFixed-point theoremFuzzy logicComplete metric spaceAlgebraMetric spaceSettore MAT/05 - Analisi Matematicacomplete metric spaceordinary fuzzy differential equationaltering distance functionContraction principleC0-semigroupDifferential algebraic equationAnalysisNumerical partial differential equationsMathematicsAdvances in Difference Equations
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Qualitative Analysis of Differential, Difference Equations, and Dynamic Equations on Time Scales

2015

and Applied Analysis 3 thank Guest Editors Josef Dibĺik, Alexander Domoshnitsky, Yuriy V. Rogovchenko, Felix Sadyrbaev, and Qi-Ru Wang for their unfailing support with editorial work that ensured timely preparation of this special edition. Tongxing Li Josef Dibĺik Alexander Domoshnitsky Yuriy V. Rogovchenko Felix Sadyrbaev Qi-Ru Wang

Article SubjectDifferential equationlcsh:MathematicsApplied MathematicsFinite difference methodlcsh:QA1-939Stochastic partial differential equationNonlinear systemMultigrid methodKolmogorov equations (Markov jump process)Simultaneous equationsApplied mathematicsAnalysisNumerical partial differential equationsMathematicsAbstract and Applied Analysis
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A comparison analysis between unsymmetric and symmetric radial basis function collocation methods for the numerical solution of partial differential …

2002

Abstract In this article, we present a thorough numerical comparison between unsymmetric and symmetric radial basis function collocation methods for the numerical solution of boundary value problems for partial differential equations. A series of test examples was solved with these two schemes, different problems with different type of governing equations, and boundary conditions. Particular emphasis was paid to the ability of these schemes to solve the steady-state convection-diffusion equation at high values of the Peclet number. From the examples tested in this work, it was observed that the system of algebraic equations obtained with the symmetric method was in general simpler to solve …

CollocationPartial differential equationSeries (mathematics)Numerical solutionMathematical analysisPartial differential equationAlgebraic equationComputational MathematicsComputational Theory and MathematicsModeling and SimulationCollocation methodModelling and SimulationRadial basis functionBoundary value problemMesh free techniqueMathematicsNumerical partial differential equationsComputers & Mathematics with Applications
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The exact finite‐difference scheme for vector boundary‐value problems with piece‐wise constant coefficients

1998

We will consider the exact finite‐difference scheme for solving the system of differential equations of second order with piece‐wise constant coefficients. It is well‐known, that the presence of large parameters at first order derivatives or small parameters at second order derivatives in the system of hydrodynamics and magnetohydrodynamics (MHD) equations (large Reynolds, Hartmann and others numbers) causes additional difficulties for the applications of general classical numerical methods. Thus, important to work out special methods of solution, the so‐called uniform converging computational methods. This gives a basis for the development of special monotone finite vector‐difference schem…

Constant coefficientsPartial differential equationDifferential equationNumerical analysisMathematical analysisOrder of accuracy-Modeling and SimulationQA1-939PiecewiseBoundary value problemMathematicsAnalysisMathematicsNumerical partial differential equationsMathematical Modelling and Analysis
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A fully adaptive wavelet algorithm for parabolic partial differential equations

2001

We present a fully adaptive numerical scheme for the resolution of parabolic equations. It is based on wavelet approximations of functions and operators. Following the numerical analysis in the case of linear equations, we derive a numerical algorithm essentially based on convolution operators that can be efficiently implemented as soon as a natural condition on the space of approximation is satisfied. The algorithm is extended to semi-linear equations with time dependent (adapted) spaces of approximation. Numerical experiments deal with the heat equation as well as the Burgers equation.

FTCS schemeNumerical AnalysisDifferential equationIndependent equationApplied MathematicsMathematical analysisMathematicsofComputing_NUMERICALANALYSISExponential integratorParabolic partial differential equationComputational MathematicsMultigrid methodAlgorithmMathematicsNumerical stabilityNumerical partial differential equationsApplied Numerical Mathematics
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Simplifying differential equations for multi-scale Feynman integrals beyond multiple polylogarithms

2017

In this paper we exploit factorisation properties of Picard-Fuchs operators to decouple differential equations for multi-scale Feynman integrals. The algorithm reduces the differential equations to blocks of the size of the order of the irreducible factors of the Picard-Fuchs operator. As a side product, our method can be used to easily convert the differential equations for Feynman integrals which evaluate to multiple polylogarithms to $\varepsilon$-form.

High Energy Physics - Theory010308 nuclear & particles physicsDifferential equationNumerical analysisGeneral Physics and AstronomyOrder (ring theory)FOS: Physical sciencesDecoupling (cosmology)Picard–Fuchs equation01 natural sciencesHigh Energy Physics - PhenomenologyOperator (computer programming)High Energy Physics - Phenomenology (hep-ph)FactorizationHigh Energy Physics - Theory (hep-th)0103 physical sciencesComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONApplied mathematics010306 general physicsMathematicsNumerical partial differential equations
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A new result on impulsive differential equations involving non-absolutely convergent integrals

2009

AbstractIn this paper we obtain, as an application of a Darbo-type theorem, global solutions for differential equations with impulse effects, under the assumption that the function on the right-hand side is integrable in the Henstock sense. We thus generalize several previously given results in literature, for ordinary or impulsive equations.

Integrable systemHenstock integralDifferential equationApplied MathematicsMathematical analysisMathematics::Classical Analysis and ODEsFixed-point theoremImpulse (physics)Absolute convergenceHenstock–Lebesgue integralSimultaneous equationsimpulsive differential equation Henstock integral Henstock-Lebesgue integral Darbo fixed point Theorem.Impulsive differential equationDarbo fixed point theoremDifferential algebraic equationAnalysisNumerical partial differential equationsMathematicsJournal of Mathematical Analysis and Applications
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Modelling of Pe C alloys solidification using the artificial heat source method

1997

Abstract In the paper the numerical solutions concerning the cast iron and also the carbon steel solidification are presented. In order to take into account the non-linearities appearing in differential equations describing the boundary-initial problem considered — a certain algorithm called the artificial heat source method has been used. The examples illustrating the possibilities of proposed method applications have been solved by means of the boundary element method, but the others numerical methods can be also utilized.

Materials scienceDifferential equationNumerical analysisMetallurgyMetals and AlloysSingular boundary methodBoundary knot methodIndustrial and Manufacturing EngineeringComputer Science ApplicationsModeling and SimulationAnalytic element methodCeramics and CompositesApplied mathematicsMethod of fundamental solutionsBoundary element methodNumerical partial differential equationsJournal of Materials Processing Technology
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DEGENERATE MATRIX METHOD FOR SOLVING NONLINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS

1998

Degenerate matrix method for numerical solving nonlinear systems of ordinary differential equations is considered. The method is based on an application of special degenerate matrix and usual iteration procedure. The method, which is connected with an implicit Runge‐Kutta method, can be simply realized on computers. An estimation for the error of the method is given. First Published Online: 14 Oct 2010

Mathematical analysisMathematicsofComputing_NUMERICALANALYSISNumerical methods for ordinary differential equationsExplicit and implicit methods-Backward Euler methodModeling and SimulationCollocation methodQA1-939Crank–Nicolson methodDifferential algebraic equationMathematicsAnalysisMathematicsMatrix methodNumerical partial differential equationsMathematical Modelling and Analysis
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