10-05-2012, 04:35 PM
Engineering Problem Solving
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Problem-Solving Process
The problem-solving process for a computational problem can be outlined as follows:
1. Define the problem.
2. Create a mathematical model.
3. Develop a computational method for solving the problem.
4. Implement the computational method.
5. Test and assess the solution.
The boundaries between these steps can be blurred and for specific problems one or two of the
steps may be more important than others. Nonetheless, having this approach and strategy in mind
will help to focus our efforts as we solve problems
Problem Definition:
The first steps in problem solving include:
• Recognize and define the problem precisely by exploring it thoroughly (may be the most
difficult step).
• Determine what question is to be answered and what output or results are to be produced.
• Determine what theoretical and experimental knowledge can be applied.
• Determine what input information or data is available
Many academic problems that you will be asked to solve have this step completed by the instructor.
For example, if your instructor ask you to solve a quadratic algebraic equation and provides you
with all of the coefficients, the problem has been completely defined before it is given to you and
little doubt remains about what the problem is.
If the problem is not well defined, considerable effort must be expended at the beginning in studying
the problem, eliminating the things that are unimportant, and focusing on the root problem. Effort
at this step pays great dividends by eliminating or reducing false trials, thereby shortening the time
taken to complete later steps.
After defining the problem:
• Collect all data and information about the problem.
• Verify the accuracy of this data and information.
• Determine what information you must find: intermediate results or data may need to be
found before the required answer or results can be found.
Mathematical Model:
To create a mathematical model of the problem to be solved:
• Determine what fundamental principles are applicable.
• Draw sketches or block diagrams to better understand the problem.
• Define necessary variables and assign notation.
• Reduce the problem as originally stated into one expressed in purely mathematical terms.
• Apply mathematical expertise to extract the essentials from the underlying physical description
of the problem.
• Simplify the problem only enough to allow the required information and results to be obtained.
• Identify and justify the assumptions and constraints inherent in this model.
Computational Method:
A computational method for solving the problem is to be developed, based on the mathematical
model.
• Derive a set of equations that allow the calculation of the desired parameters and variables.
• Develop an algorithm, or step-by-step method of evaluating the equations involved in the
solution.
• Describe the algorithm in mathematical terms and then implement as a computer program.
• Carefully review the proposed solution, with thought given to alternative approaches.
Implementation ofComputational Method:
Once a computational method has been identified, the next step is to carry out the method with a
computer, whether human or silicon.
Some things to consider in this implementation:
• Assess the computational power needed, as an acceptable implementation may be hand calculation
with a pocket calculator.
• If a computer program is required, a variety of programming languages, each with different
properties, are available.
• A variety of computers, ranging from the most basic home computers to the fastest parallel
supercomputers, are available.