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FINITE DIFFERENCE METHODS FOR SOLVING DIFFERENTIAL …

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FINITE DIFFERENCE METHODSFORSOLVING DIFFERENTIAL EQUATIONSI-Liang ChernDepartment of MathematicsNational Taiwan UniversityMay 16, 20132Contents1 FINITE DIFFERENCE Approximation . . . . . . . . . . . . . . . . . . .. . . . . . . . Basic Numerical METHODS for Ordinary DIFFERENTIAL equations . . . . . . . . . . . Runge-Kutta METHODS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . Multistep METHODS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . Linear DIFFERENCE equation . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . Stability analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . Zero Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .182 FINITE DIFFERENCE METHODS for Linear Parabolic FINITE DIFFERENCE METHODS for the Heat Equation.

The goal of this course is to provide numerical analysis background for finite difference methods for solving partial differential equations. The focuses are the stability and convergence theory. The partial differential equations to be discussed include •parabolic equations, •elliptic equations, •hyperbolic conservation laws.

  Methods, Differential, Equations, Differential equations

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