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A functional equation is called stable if any approximately solution to the functional equation is near to a true solution of that functional equation, and is superstable if every approximately solution is an exact solution of it.
Also, if every approximately solution is an exact solution of it, we say the functional equation is superstable (see, [1]).
We say that a functional equation is superstable if every approximately solution of is an exact solution of it (see [1]).
One should remember that the functional equation is called stable if any approximately solution to the functional equation is near to a true solution of that functional equation, and is supersuperstable if every approximately solution is an exact solution of it (see [14]).
By employing the least-square method, we can search for the "approximately" solution of ϕ and φ as left{begin{array}{l}phi =0.25times left( arccos left({p}_{i1}+{p}_{i2}right)+ arccos left({p}_{i1}-{p}_{i2}right)+left.
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Table 1 presents the error between exact and approximately solutions of NBVP.
Theorem 2.3 means that an approximately optimal solution to [SP] is an approximately optimal solution to [P] if the solution to [SP] is ϵ-feasible.
Theorem 2.1 and Theorem 2.2 mean that an approximately optimal solution to [SP] is also an approximately optimal solution to ([LOP^{prime}]_{k}) when the error ϵ is sufficiently small.
Based on the averaging method, the approximately analytical solution and the amplitude frequency equation are obtained.
Moreover, the comparisons of the amplitude frequency curves obtained by the approximately analytical solution and the numerical integration are fulfilled, and the results certify the correctness and satisfactory precision of the approximately analytical solution.
Applying the periodic properties of the boundary condition, an approximately analytical solution for heat transfer is obtained.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com