2.2 APROXIMATING METHODS
It is possible to obtain exact analytical solutions for few simplified engineering problems. The exact solution can be obtained by direct integration of the concerned differential equations. Generally, the direct integration is made possible by: (i) separation of variables; (ii) similarity solutions; or (iii) Fourier and Laplace transformations. Since most engineering problems are complex in nature, number of problems having exact solutions is severely limited. Hence, approximate solutions are generally sought.
Generally used approximating methods are as follows.
- Perturbation Techniques
- Power Series Solutions
- Probability Methods
- Finite Difference Method (FDM)
- Method of Weighted Residuals (MWR)
- Rayleigh–Ritz Method
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