Abstract
In this paper we study the deviation of the error estimation for the second order Fredholm-Volterra integro-differential equations. We prove that for m degree piecewise polynomial collocation method, our method provides O(hm+1) as the order of the deviation of the error. Also numerical results in the final section are included to confirm the theoretical results.
Highlights
In this paper we consider the second order Fredholm-Volterra integrodifferential (SFVID) equations as follows where y (t) = F t, y(t), y (t), zf [y](t), zv[y](t), t ∈ I := [a, b], y(a) = r1, y(b) = r2, zf [y](t) = zv[y](t) = bKf t, s, y(s), y (s), y (s) ds, a tKv t, s, y(s), y (s), y (s) ds a (1.1) (1.2)R
We show that in this case for m degree piecewise polynomial collocation method, our method provides O(hm+2) as the order of the deviation of the error
We introduce some details about the deviation of the error estimation, collocation method, finite differences and exact difference schemes
Summary
In the nonlinear case we assume that F t, y, y , zf , zv , Fl t, y, y , zf , zv for any l = t, y, y , zf , zv are Lipschitz-continuous. We say SFVID equation with boundary condition (1.2) is linear if we can write (1.1) as follows y (t) = a1(t)y (t) + a2(t)y(t) + a3(t) + zf [y](t) + zv[y](t), t ∈ [a, b] (1.3). In the linear case we assume that ai(t), i = 1, 2, 3 are sufficiently smooth in I. The deviation of the error estimation for linear and nonlinear first and second order boundary value problem is studied in [1, 2, 3]. A summary is given at the end of the paper in Conclusion section
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