19. ch11.3 Finite-Difference Methods for Linear...

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Chapter 11.3:Finite-Difference MethodsforLinear ProblemsDr. AlharbiTaibah University, Mathematics DepartmentBoundary-Value Problemsfor Ordinary Differential EquationsNumerical Analysis,Ninth Edition,R. Burden and J. Faires
Finite-Difference Methods for Linear ProblemsThe linear and nonlinear Shooting methods for boundary-value problems can present problems of instability.The methods in this section have better stabilitycharacteristics.However, they generally require more computation to obtain aspecified accuracy.Methods involving finite differences for solving boundary-value problems replace each of the derivatives in thedifferential equation with an appropriate difference-quotientapproximationof the type considered in Section 4.1.The particular difference quotient and???? ?𝑖?? ℎare chosento maintain a specified order oftruncation error.However,cannot be chosen too small because of thegeneral instability of the derivative approximations.Discrete ApproximationThe finite difference method for the linear second-orderboundary-value problem,

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Term
Fall
Professor
Covill
Tags
Numerical Analysis, finite difference, Finite difference method, linear problems

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