Omar_Absi
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In this example, A0 would be the known solution to the exactly solvable initial problem and A1,A2,... represent the "higher orders" which are found iteratively by some systematic procedure. For small ε these higher orders are presumed to become successively less important.
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From Wikipedia
Perturbation theory comprises mathematical methods that are used to find an approximate solution to a problem which cannot be solved exactly, by starting from the exact solution of a related problem. Perturbation theory is applicable if the problem at hand can be formulated by adding a "small" term to the mathematical description of the exactly solvable problem.
Perturbation theory leads to an expression for the desired solution in terms of a power series in some "small" parameter that quantifies the deviation from the exactly solvable problem. The leading term in this power series is the solution of the exactly solvable problem, while further terms describe the deviation in the solution, due to the deviation from the initial problem. Formally, we have for the approximation to the full solution A, a series in the small parameter (here called ε), like the following:
Perturbation theory leads to an expression for the desired solution in terms of a power series in some "small" parameter that quantifies the deviation from the exactly solvable problem. The leading term in this power series is the solution of the exactly solvable problem, while further terms describe the deviation in the solution, due to the deviation from the initial problem. Formally, we have for the approximation to the full solution A, a series in the small parameter (here called ε), like the following:
In this example, A0 would be the known solution to the exactly solvable initial problem and A1,A2,... represent the "higher orders" which are found iteratively by some systematic procedure. For small ε these higher orders are presumed to become successively less important.
For more information see the link below
http://en.wikipedia.org/wiki/Perturbation_theory
and for perturbation methods see the following link
http://www.sm.luth.se/~tomas/applmath/chap2en/index.html
http://en.wikipedia.org/wiki/Perturbation_theory
and for perturbation methods see the following link
http://www.sm.luth.se/~tomas/applmath/chap2en/index.html
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