Assume that a numerical method possesses an asymptotic error expansion of the form Îh – y(T) = Dhº +O(hP+1) T obtained with step size h, and D is a where yh is the approximate solution at time t constant. If one uses the numerical method to create approximate solutions to a problem where the exact solution is known, i.e. y(T) is known, derive a formula for an estimate of the order of accuracy (which we also call the rate of convergence) p that is based upon the results of two computations, one using h = known, you can have y(T) in the formula.] %3D h and one using h = . [Hints: since y(T) is %3D
Assume that a numerical method possesses an asymptotic error expansion of the form Îh – y(T) = Dhº +O(hP+1) T obtained with step size h, and D is a where yh is the approximate solution at time t constant. If one uses the numerical method to create approximate solutions to a problem where the exact solution is known, i.e. y(T) is known, derive a formula for an estimate of the order of accuracy (which we also call the rate of convergence) p that is based upon the results of two computations, one using h = known, you can have y(T) in the formula.] %3D h and one using h = . [Hints: since y(T) is %3D
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.5: Iterative Methods For Solving Linear Systems
Problem 20EQ
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