Search results for "First-order partial differential equation"

showing 10 items of 18 documents

A third order partial differential equation for isotropic boundary based triangular Bézier surface generation

2011

Abstract We approach surface design by solving a linear third order Partial Differential Equation (PDE). We present an explicit polynomial solution method for triangular Bezier PDE surface generation characterized by a boundary configuration. The third order PDE comes from a symmetric operator defined here to overcome the anisotropy drawback of any operator over triangular Bezier surfaces.

Bézier surfaceSurface (mathematics)PolynomialPartial differential equationPDE surfaceOperator (physics)Applied MathematicsMathematical analysisFirst-order partial differential equationBoundary (topology)Partial differential equationIsotropyPDE surfaceComputational MathematicsComputer Science::GraphicsBézier triangleExplicit solutionMathematicsJournal of Computational and Applied Mathematics
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Generalized finite difference schemes with higher order Whitney forms

2021

Finite difference kind of schemes are popular in approximating wave propagation problems in finite dimensional spaces. While Yee’s original paper on the finite difference method is already from the sixties, mathematically there still remains questions which are not yet satisfactorily covered. In this paper, we address two issues of this kind. Firstly, in the literature Yee’s scheme is constructed separately for each particular type of wave problem. Here, we explicitly generalize the Yee scheme to a class of wave problems that covers at large physics field theories. For this we introduce Yee’s scheme for all problems of a class characterised on a Minkowski manifold by (i) a pair of first ord…

Differential equationDifferential formsähkömagnetismiFirst-order partial differential equationdifferential formselectromagnetism010103 numerical & computational mathematics01 natural sciencesdifferentiaaligeometriaMinkowski spaceApplied mathematicsdifferential geometry0101 mathematicsFinite setfinite difference methodMathematicsNumerical AnalysisSpacetimeApplied MathematicsFinite difference methodFinite differencevector-valued formswhitney forms010101 applied mathematicsComputational MathematicsModeling and Simulationelasticityco-vector valued formsAnalysisESAIM: Mathematical Modelling and Numerical Analysis
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Direct Derivation of Corrective Terms in SDE Through Nonlinear Transformation on Fokker–Planck Equation

2004

This paper examines the problem of probabilistic characterization of nonlinear systems driven by normal and Poissonian white noise. By means of classical nonlinear transformation the stochastic differential equation driven by external input is transformed into a parametric-type stochastic differential equation. Such equations are commonly handled with Ito-type stochastic differential equations and Ito's rule is used to find the response statistics. Here a different approach is proposed, which mainly consists in transforming the Fokker–Planck equation for the original system driven by external input, in the transformed probability density function of the new state variable. It will be shown …

Kushner equationDifferential equationApplied MathematicsMechanical EngineeringNonlinear transformationMathematical analysisFirst-order partial differential equationFokker-Planck equationAerospace EngineeringOcean EngineeringPoisson inputItô's calculuIntegrating factorStochastic partial differential equationStochastic differential equationQuantum stochastic calculusControl and Systems EngineeringApplied mathematicsFokker–Planck equationStochastic differential calculusElectrical and Electronic EngineeringMathematicsNonlinear Dynamics
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A theorem of Radò’s type for the solutions of a quasi-linear equation

2004

Laplace's equationPartial differential equationLinear differential equationDifferential equationGeneral MathematicsMathematical analysisFirst-order partial differential equationRiccati equationHeat equationUniversal differential equationMathematicsMathematical Research Letters
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Explicit polynomial solutions of fourth order linear elliptic Partial Differential Equations for boundary based smooth surface generation

2011

We present an explicit polynomial solution method for surface generation. In this case the surface in question is characterized by some boundary configuration whereby the resulting surface conforms to a fourth order linear elliptic Partial Differential Equation, the Euler–Lagrange equation of a quadratic functional defined by a norm. In particular, the paper deals with surfaces generated as explicit Bézier polynomial solutions for the chosen Partial Differential Equation. To present the explicit solution methodologies adopted here we divide the Partial Differential Equations into two groups namely the orthogonal and the non-orthogonal cases. In order to demonstrate our methodology we discus…

Mathematical analysisFirst-order partial differential equationExplicit and implicit methodsAerospace EngineeringPartial differential equationExplicit polynomial solutionExponential integratorComputer Graphics and Computer-Aided DesignParabolic partial differential equationSurface generationPDE surfaceLinear differential equationElliptic partial differential equationModeling and SimulationAutomotive EngineeringSymbol of a differential operatorMathematicsComputer Aided Geometric Design
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Multiscale Particle Method in Solving Partial Differential Equations

2007

A novel approach to meshfree particle methods based on multiresolution analysis is presented. The aim is to obtain numerical solutions for partial differential equations by avoiding the mesh generation and by employing a set of particles arbitrarily placed in problem domain. The elimination of the mesh combined with the properties of dilation and translation of scaling and wavelets functions is particularly suitable for problems governed by hyperbolic partial differential equations with large deformations and high gradients.

Multiresolution analysiMethod of linesMathematical analysisFirst-order partial differential equationExponential integratorSPH methodStochastic partial differential equationSettore ING-IND/31 - ElettrotecnicaSettore MAT/08 - Analisi NumericaMultigrid methodMethod of characteristicsMeshfree particle methodHyperbolic partial differential equationNumerical partial differential equationsMathematicsAIP Conference Proceedings
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A FAMILY OF THE SPIRAL SOLUTIONS OF THE NONLINEAR KLEIN‐GORDON EQUATION

1998

A family of the functions, intended for a construction the exact travelling wave solutions of nonlinear partial differential equations, is given. Exact solutions of the Klein‐Gordon equation with a special potential are obtained. The behavior of complex and hypercomplex solutions of the second order is presented. First Published Online: 14 Oct 2010

Partial differential equationDifferential equationFirst-order partial differential equationExact differential equation-Kadomtsev–Petviashvili equationParabolic partial differential equationsymbols.namesakeModeling and SimulationQA1-939symbolsFisher's equationHyperbolic partial differential equationMathematicsAnalysisMathematical physicsMathematicsMathematical Modelling and Analysis
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Walsh function analysis of 2-D generalized continuous systems

1990

The importance of the generalized or singular 2D continuous systems are demonstrated by showing their use in the solution of partial differential equations in two variables. A technique is presented for solving these systems in terms of Walsh functions. The method replaces the solution of a two-variable partial differential equation with the solution of a linear algebraic generalized 2D Sylvester equation. An efficient technique for the recursive solution of the latter equation is offered. All the results apply also in the usual Roesser 2D state-space case. >

Partial differential equationDifferential equationWeak solutionMathematical analysisMathematicsofComputing_NUMERICALANALYSISFirst-order partial differential equationParabolic partial differential equationComputer Science ApplicationsMethod of characteristicsControl and Systems EngineeringComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONElectrical and Electronic EngineeringSylvester equationUniversal differential equationMathematicsIEEE Transactions on Automatic Control
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Partial differential equations and quasiregular mappings

1992

Partial differential equationMathematical analysisFirst-order partial differential equationMathematics
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Stochastic Kinetics with Wave Nature

2003

We consider stochastic second-order partial differential equations. We indroduce a noisy non-linear wave equation and discuss its connections, in particular via the Lorentz transformation, with known stochastic models.

PhysicsStochastic partial differential equationContinuous-time stochastic processStochastic differential equationQuantum stochastic calculusStochastic modellingDifferential equationFirst-order partial differential equationStatistical and Nonlinear PhysicsStatistical physicsPhysics::Classical PhysicsCondensed Matter PhysicsHyperbolic partial differential equationModern Physics Letters B
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