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You cannot apply traditional methods such as integrating-by-parts or integrating-by-substitution to solve for a closed form solution. If you try to find a closed-form analytical solution to the above equation, do not bother there is none. The advantage of numerical computation is that a numerical answer to a specific model problem can always be obtained even when it has no analytic solution at all. The efficiency can be measured by the number of steps in the algorithm, CPU time, and the amount of memory allocated for a specific numerical computation. A numeric computation software developer is not just interested in computing the answer for a problem, but also the best or optimal algorithm that gets there in the most efficient way. An algorithm is used in a systematic way that solves a problem.
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Numerical computation is the study and devising of procedures, methods, and functions for solving problems with a computer.
![Program for bisection method in fortran compilers](https://kumkoniak.com/115.png)