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Exact(5)
The exact solution of this example is not available.
Also, Figure 5 shows the exact and the approximate solution of this example.
Figure 3 shows the exact and approximate solution of this example.
Figure 1 shows the exact and the approximate solution of this example.
end{aligned} (30 Finally, the exact solution of this example is: begin{aligned} mathcal {Z}_{t}=ln (X_{t})=ln left( frac{1}{2} hbox {e}^{2Y_{t}}right) =2Y_{t}-ln 2=ln 2lexp( exp left( W^Q_{t}-frac{3t}{2} right) -1right).
Similar(55)
We can see that the solutions of this example are δ-independent.
} end{aligned} (25)from (9), we can get immediately (E[X]=X_0(mathcal {Z}_t^{lambda })^{-1}) such that (lambda =frac{a(t)}{b(t)}.) The graphs of various numerical solutions of this example by Milstein method, proposed formula (11) that is drift free and Taylor method of order (2) introduced as exact solution.
By using two types of cutting plane methods developed by Ren and Wang [25], the best and worst optimal solutions of this example is finally obtained as ((16,11)) and ((7,2)), and the corresponding upper objective function values are ([-11,38] [-11,38]2,11]).
The aim of the paper is to prove the exactness of the solution for this example by comparing it to step-by-step computations of the elastoplastic response of the body under repeated cyclic loads of increasing level.
Figure 2 Exact and approximate solution of the example.
The respective exact solution of the example is found using a commercial solver (CPLEX).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com