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It is required to evaluate the gradient of the function f (x1, x2) = 100(x2 - x})² + (1 – x1)² at point X = {} using a finite-difference scheme. Determine the step size Ax to be used to limit the error in any of the components, af/ax¡, to 1 % of the exact value, in the following methods: (a) Central difference method (b) Forward difference method (c) Backward difference method

It is required to evaluate the gradient of the function f (x1, x2) = 100(x2 - x})² + (1 – x1)² at point X = {} using a finite-difference scheme. Determine the step size Ax to be used to limit the error in any of the components, af/ax¡, to 1 % of the exact value, in the following methods: (a) Central difference method (b) Forward difference method (c) Backward difference method

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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6.34 It is required to evaluate the gradient of the function f(x1, x2) = 100(x2 – xỉ)² + (1 – x1)² at point X = {03} using a finite-difference scheme. Determine the step size Ax to be used to limit the error in any of the components, af/ax;, to 1 % of the exact value, in the following methods: (a) Central difference method (b) Forward difference method (c) Backward difference method
Transcribed Image Text:6.34 It is required to evaluate the gradient of the function f(x1, x2) = 100(x2 – xỉ)² + (1 – x1)² at point X = {03} using a finite-difference scheme. Determine the step size Ax to be used to limit the error in any of the components, af/ax;, to 1 % of the exact value, in the following methods: (a) Central difference method (b) Forward difference method (c) Backward difference method
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