Search results for "Numerical methods for ordinary differential equations"

showing 2 items of 2 documents

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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