Abstract
We use the Polynomial Least Squares Method (PLSM), which allows us to compute analytical approximate polynomial solutions for nonlinear ordinary differential equations with the mixed nonlinear conditions. The accuracy of the method is illustrated by a comparison with approximate solutions previously computed using Bernstein polynomials method.
Highlights
Pm(t) = c0 + c1t + c2t2 + · · · + cmtm, ci ∈ R, i = 0, 1, · · · , m αPm(a) + βPm(b) + γ(Pm(a))2 + τ (Pm(b))2 + ξPm(a)Pm(b) = λ lim m→∞
(iii) R(t) = −3t6 − t(d1 + 2d2t + 3d3t2) − 3(1 + d1t + d2t2 + d3t3)+ + 3(1 + d1t + d2t2 + d3t3)2.
XP LSM = 1 + 0.721523t + 0.939892t2.
Summary
Pm(t) = c0 + c1t + c2t2 + · · · + cmtm, ci ∈ R, i = 0, 1, · · · , m αPm(a) + βPm(b) + γ(Pm(a))2 + τ (Pm(b))2 + ξPm(a)Pm(b) = λ lim m→∞
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