Search results for "Exponential integrator"

showing 4 items of 4 documents

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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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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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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