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Published on Aug View Download The following Fortran 90 program is one example. It should be noted that the availability of complex variables in Fortran 90, would allow this metodoz to be made even more concise. Several features of this subroutine bear mention: The subroutine does not involve input or output. Rather, information is passed in and out via the arguments.

M̩todos num̩ricos para ingenieros (5a. ed.). РSteven C. Chapra, Raymond P. Canale РGoogle Books

The following algorithm implements this summation: Input value to be evaluated x and maximum order n Step 3: Set order i equal to one Step 4: Set accumulator for approximation approx to zero Step 5: Set accumulator mteodos factorial product fact equal to one Step 6: Calculate true value of sin x Step 7: If order is greater than n then proceed to step 13 Otherwise, proceed to next step Step 8: Increment ilbro order chapea one Step Return to step 7 Step This occurs because of round-off error, which will be discussed in Chap.

The following pseudocode provides an algorithm to program this problem. Notice that the input of the quizzes and homeworks is done with logical loops that terminate when the user enters a negative grade: This invokes the function procedure so that the friction factor is determined at each iteration.

The resulting final solution is Notice that we have named the cells containing the parameter values with numerucos labels in column A. The result is Notice that we have rearranged the two functions so that the correct values will drive them both to zero.


We then drive the sum of their squared values to zero by varying x and y.

Solucionario Metodos Numericos para Ingenieros Chapra y Canale 5 edicion

The result is 7. The Solver set up is shown below using initial guesses of 1. The result is For guesses of 1.

This establishes the link to the IMSL libraries II Using the Roots Function: The nujericos functions can be set up as roots problems: The roots of the denominator are: Select Next j ActiveCell. Select Next i Range “a1”. Matlab solution to Prob. Matrix is close to singular or badly scaled. Results may be inaccurate. A lda,lda ,Rcond,Res n Real:: Jetodos n,nfac n,nRcond, res n Real:: Select Next i Range “a3”. However a sample of initial guesses spanning liro range yield the following roots: Although some follow the pattern, others jump to roots that are far away.

For example, the guess of -6, 0 jumps to the root in the first quadrant. This libo the notion that root location techniques are highly sensitive to initial guesses and that open methods like the Solver can locate roots that are not in the vicinity of the initial guesses. However, if Set 1 and 3 are reordered so that they are diagonally dominant, they will converge on the solution of 1, 1, 1.

Solucionario Metodos Numericos para Ingenieros Chapra y Canale 5 edicion

However, since it is close to being diagonally dominant, a solution can be obtained by the following ordering: Therefore, a tridiagonal solver is well worth using. N aaaa baba x N aaaa baba x Excel Solver can be used to solve the problem: Change B0 to This problem can be set up on Excel and the answer generated with Solver: The solution is Note that we have named the cells with the labels in the adjacent left columns. Our goal is to minimize the wetted perimeter by varying the depth and width.

We apply positivity constraints along with the constraint that the computed area must equal the desired area. The result is Thus, this specific application indicates that a 45o angle yields the minimum wetted perimeter.


The verification of whether this result is universal can be attained inductively or deductively.

The inductive approach involves trying several different desired areas in conjunction with our solver solution. As long as the desired area is greater chapa 0, the result for the optimal design will be 45o. The deductive verification involves calculus. The minimum wetted perimeter should occur when the derivative of the perimeter with respect to one of the primary dimensions i.

That is, the slope is zero. In the case of the width, this would be expressed by: To formulate P in terms of w, substitute Eqs. The following formulas can be mrtodos Our goal is to minimize the llibro perimeter by varying the depth, width and theta the angle. The result is Thus, this specific application indicates that a 60o angle yields the minimum wetted perimeter.

Because of the presence of 1 s in the denominator, the function will experience a division by zero at the maximum. However, if we assume that the function has one maximum and no minima within the interval, a check can be included.

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