- Lookup Tables: Many inverse Laplace transforms can be computed using predefined tables of Laplace transform pairs. If the symbolic expression matches a known form, the corresponding time-domain function can be returned.
- Partial Fraction Expansion: For rational expressions, the inverse Laplace transform can be found by performing a partial fraction expansion followed by applying the inverse Laplace transform to each term individually, which often corresponds to a known transform pair.
- Complex Integration: The inverse Laplace transform can be theoretically computed by evaluating a Bromwich integral, which is a contour integral in the complex plane. However, this method is usually not used in symbolic computation software due to its complexity.
- Algorithms for Symbolic Integration: Many times, the problem of finding an inverse Laplace transform reduces to a symbolic integration problem. MATLAB's symbolic engine includes algorithms to perform integration symbolically, which could be applied to solve inverse Laplace transform problems.
- Numerical Inversion: When a symbolic solution is difficult to obtain, numerical techniques may be employed to approximate the inverse Laplace transform. However, this is less common in a purely symbolic context.
In practice, the ilaplace function likely uses a combination of these methods, with a heavy reliance on lookup tables and symbolic algebra techniques to simplify expressions and find corresponding time-domain functions. If you need the exact details of the algorithm, you might have to contact MathWorks support directly, although they may not provide specifics if it's proprietary information.
---------------------------------------------------------------------------------------------------------------------------------------------------
If you find the solution helpful and it resolves your issue, it would be greatly appreciated if you could accept the answer. Also, leaving an upvote and a comment are also wonderful ways to provide feedback.
Professional Interests
- Technical Services and Consulting
- Embedded Systems | Firmware Developement | Simulations
- Electrical and Electronics Engineering
Feel free to contact me.
