Search results for "Explicit and implicit methods"

showing 3 items of 3 documents

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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Minimally implicit Runge-Kutta methods for Resistive Relativistic MHD

2016

The Relativistic Resistive Magnetohydrodynamic (RRMHD) equations are a hyperbolic system of partial differential equations used to describe the dynamics of relativistic magnetized fluids with a finite conductivity. Close to the ideal magnetohydrodynamic regime, the source term proportional to the conductivity becomes potentially stiff and cannot be handled with standard explicit time integration methods. We propose a new class of methods to deal with the stiffness fo the system, which we name Minimally Implicit Runge-Kutta methods. These methods avoid the development of numerical instabilities without increasing the computational costs in comparison with explicit methods, need no iterative …

AstrofísicaHistoryResistive touchscreenPartial differential equation010308 nuclear & particles physicsExplicit and implicit methodsNumerical methods for ordinary differential equationsStiffnessMagnetohidrodinàmica01 natural sciencesComputer Science ApplicationsEducationRunge–Kutta methods0103 physical sciencesmedicineCalculusApplied mathematicsMagnetohydrodynamic driveMagnetohydrodynamicsmedicine.symptom010303 astronomy & astrophysicsMathematics
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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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