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The RKHSM for solving neutral functional-differential equations with proportional delays. (English) Zbl 1267.34133

Summary: We consider the following neutral functional-differential equations with proportional delays

(u(t)+a(t)u(p m t)) (m) =βu(t)+ k=0 m-1 b k (t)u (k) (p k t)+f(t),t0,(1)

with the initial conditions

k=0 m-1 c ik u (k) (0)=λ i ,i=0,1,,m-1·(2)

The reproducing kernel Hilbert space method (RKHSM) is applied to (1), (2). Its approximate solution is obtained by truncating the n-term of exact solution. Some examples are displayed to demonstrate the computation efficiency of the method. We also compare the performance of the method with a particular Runge-Kutta method, a one-leg θ-method and variational iteration method. Experimental results indicate that the RKHSM is an accurate and efficient method for the solution of neutral functional-differential equations with proportional delays.

MSC:
34K28Numerical approximation of solutions of functional-differential equations
34K06Linear functional-differential equations