CHE110_NewtonRaphsonVBA

CHE110_NewtonRaphsonVBA - Rose-Hulman Institute of...

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Rose-Hulman Institute of Technology Department of Chemical Engineering CHE 110 - Introduction to Programming & Problem Solving Spring 2006 Workshop 2: Creating a Customized VBA Worksheet Function to Solve a Nonlinear Algebraic Equation by the Newton-Raphson Method Background Nonlinear algebraic equations are frequently encountered in a variety of engineering problems. The Newton-Raphson method is the most common numerical technique applied to solving nonlinear equations. Consider a single nonlinear equation in canonical form, f(x) = 0. The Newton-Raphson method is based on an approximation of f(x) using a truncated Taylor’s series expansion about some value, x o . () () () o oo x df fx fx x x 0 dx ≈+ × = This can be rearranged explicitly in terms of x, and a resulting Newton-Raphson iteration scheme is formulated. i i i1 i x fx xx df dx + =− This iteration scheme is depicted in the picture below. The slope of f(x) is used to select an updated value for x with each iteration.
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This note was uploaded on 03/08/2009 for the course CHE 110 taught by Professor Coronell during the Spring '09 term at Rose-Hulman.

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CHE110_NewtonRaphsonVBA - Rose-Hulman Institute of...

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