Abstract
Many known methods fail in the attempt to get analytic solutions of Blasius-type equations. In this work, we apply the reproducing kernel method for ivestigating Blasius equations with two different boundary conditions in semi-infinite domains. Convergence analysis of the reproducing kernel method is given. The numerical approximations are presented and compared with some other techniques, Howarth's numerical solution and Runge-Kutta Fehlberg method.
Highlights
Many approximate methods were introduced for the analytical solution of nonlinear differential equations in the recent years
We present two forms of the Blasius equation arising in fluid flow inside the velocity boundary layer as follows
We have shown comparison tables to prove the power of the reproducing kernel method (RKM)
Summary
V, h ∈ W24[0, ∞) and v(t), Ry(t) W24 = v(0)Ry(0) + v′(0)Ry′ (0) + v′′(0)Ry′′(0) + v(3)(0)Ry(3)(0). A function Ry is obtained as: We obtain v(4)(t)Ry(4)(t)dt, v, Ry W24 = v(0)Ry(0) + v′(0)Ry′ (0). On defining the linear operator L : W24[0, ∞) → W21[0, 1] as. The L given by (14) is a bounded linear operator. We have [(Lv) (t)]2 dt ≤ M12 v (Lv)′(t) = v(·), (LRt)′(·) W24 , by reproducing property. We get (Lv)′(t) ≤ v W24 (LRt)′ W24 = M2 u W24 , where M2 > 0 is positive. Where M = M12 + M22 > 0 is a positive constant
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