In this paper, we study some singular singularly-perturbed boundary-value problem Pε consisting of the differential equations and the boundary conditions where t ∈ [0, 1], 0 <ε ≤ ε0. U, V, H1 and H2 are scalar...In this paper, we study some singular singularly-perturbed boundary-value problem Pε consisting of the differential equations and the boundary conditions where t ∈ [0, 1], 0 <ε ≤ ε0. U, V, H1 and H2 are scalar functions and infinitely differentiable with respect to their variables respectively.Our approach is somewhat similar to those of Chang [2], Shi [6] and Smith [7]. Our main result (Theorem 4) is new and extends the result, in the scalar case, of Shi [6], who dealt with the problem (1) with V(t, x, ε2y, ε) in place of V(t, x, εy, ε). An application of our result is given at the end.展开更多
A numerical treatment for self-adjoint singularly perturbed second-order two-point boundary value problems using trigonometric quintic B-splines is presented,which depend on different engineering applications.The meth...A numerical treatment for self-adjoint singularly perturbed second-order two-point boundary value problems using trigonometric quintic B-splines is presented,which depend on different engineering applications.The method is found to have a truncation error of O(h 6)and converges to the exact solution at O(h 4).The numerical examples show that our method is very effective and the maximum absolute error is acceptable.展开更多
文摘In this paper, we study some singular singularly-perturbed boundary-value problem Pε consisting of the differential equations and the boundary conditions where t ∈ [0, 1], 0 <ε ≤ ε0. U, V, H1 and H2 are scalar functions and infinitely differentiable with respect to their variables respectively.Our approach is somewhat similar to those of Chang [2], Shi [6] and Smith [7]. Our main result (Theorem 4) is new and extends the result, in the scalar case, of Shi [6], who dealt with the problem (1) with V(t, x, ε2y, ε) in place of V(t, x, εy, ε). An application of our result is given at the end.
文摘A numerical treatment for self-adjoint singularly perturbed second-order two-point boundary value problems using trigonometric quintic B-splines is presented,which depend on different engineering applications.The method is found to have a truncation error of O(h 6)and converges to the exact solution at O(h 4).The numerical examples show that our method is very effective and the maximum absolute error is acceptable.
