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Solving Non-Linear Equations

# Solving Non-Linear Equations - Solving A System of...

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Solving A System of Non-linear Equations Solving Nonlinear Equations with a single variable: x 3 /60 - x = 5 sin(x) f 1 x () x 3 60 x  f 2 x ( ) 5 sin x  f 3 x f 1 x () f 2 x  The task is to find values of x for which f 1 = f 2 This is equivalent to finding values of x for which f 1 - f 2 = 0 Here's the graphical solution to the problem: 10 50 51 0 10 5 0 5 10 f 1 x f 2 x f 3 x x x1 0  root f 3 x ()x  8.8522 <= Here's the solution using the solve function. The value of the initial guess determines which root Mathcad will find. x 6  root f 3 x 5.73899 x 0  root f 3 x 0 x 4  root f 3 x 3.7535 x 6  root f 3 x 5.73899 x 10  root f 3 x 8.8522

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Here's Newton's method for solving the equation numerically: This is a simpler relative of the method mathcad uses in the
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Solving Non-Linear Equations - Solving A System of...

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