HANDBOOK OFINTEGRAL EQUATIONS phần 10 pptx

... dp 1 sin(a/p) √ p 1 √ πx sinh  √ 2ax  sin  √ 2ax  2 sin(a/p) p √ p 1 √ πa cosh  √ 2ax  sin  √ 2ax  3 cos(a/p) √ p 1 √ πx cosh  √ 2ax  cos  √ 2ax  4 cos(a/p) p √ p 1 √ πa sinh  √ 2ax  cos  √ 2ax  5 1 √ p exp  – √ ap  sin  √ ap  1 √ πx sin  a 2x  6 1 √ p exp  – √ ap  cos  √ ap  1 √ πx cos  a 2x  7 arctan a p 1 x sin(ax) 8 1 p arctan a p Si(ax) 9 p arctan a p – a 1 x...

Ngày tải lên: 23/07/2014, 16:20

... Complete Singular Integral Equations Solvable in a Closed Form In contrast with characteristic equations and their transposed equations, complete singular integral equations cannot be solved ... nonlinear integral equations with variable limits of integration are considered in Chapter 5. 14.1-2. Nonlinear Equations With Constant Integration Limits Nonlinear integral equations wit...

Ngày tải lên: 23/07/2014, 16:20

... Prior to reading this section looking through Sections 10. 4 and 10. 5 is recommended. Page 551 © 1998 by CRC Press LLC © 1998 by CRC Press LLC 11 .10- 3. The General Scheme of the Method. The Factorization ... are similar to those made above for the equations with two kernels in Subsection 11.9-2. Remark 2. Equations treated in Section 11.9 are sometimes called characteristic equation...

Ngày tải lên: 23/07/2014, 16:20

... LLC Chapter 10 Methods for Solving Linear Equations of the Form  b a K(x, t)y(t) dt = f(x) 10. 1. Some Definition and Remarks 10. 1-1. Fredholm Integral Equations of the First Kind Linear integral equations ... known. Below we list some classes of integral equations that can be reduced to ordinary differential equations with constant coefficients. 9.7-1. Equations With Kernel...

Ngày tải lên: 23/07/2014, 16:20

... Solutions: y 1 (t)= √ A, y 3 (t)= √ A (3t – 2), y 5 (t)= √ A (10t 2 – 12t + 3), y 2 (t)=– √ A, y 4 (t)=– √ A (3t – 2), y 6 (t)=– √ A (10t 2 – 12t + 3). 2 ◦ . The integral equation has some other ... roots of the quadratic equation Aβ 2 + λβ – Bλ =0. 6.2. Equations With Quadratic Nonlinearity That Contain Arbitrary Functions 6.2-1. Equations of the Form  b a G(···) dt = F (x) 1.  b a g(...

Ngày tải lên: 23/07/2014, 16:20

... special case of equation 4.9.17 with g(x)=K µ (x) and h(t)=K ν (t). 4.9. Equations Whose Kernels Contain Arbitrary Functions 4.9-1. Equations With Degenerate Kernel: K(x, t)=g 1 (x)h 1 (t)+···+ g n (x)h n (t) 1. ... cot(βt). 53. y(x) – λ  b a [A + B(x – t) cot(βx)]y(t) dt = f (x). This is a special case of equation 4.9 .10 with h(x) = cot(βx). 4.5-5. Kernels Containing Combinations of...

Ngày tải lên: 23/07/2014, 16:20

... µ) . • Reference: P. P. Zabreyko, A. I. Koshelev, et al. (1975). 3.8. Equations Whose Kernels Contain Arbitrary Functions 3.8-1. Equations With Degenerate Kernel 1.  b a  g 1 (x)h 1 (t)+g 2 (x)h 2 (t)  y(t) ... Wiener–Hopf equation of the first kind. This equation is discussed in Subsection 10. 5-1 in detail. 3.8-4. Other Equations of the Form  b a K(x, t)y(t) dt = F (x) 17.  ∞...

Ngày tải lên: 23/07/2014, 16:20

... form y(x)= m  k=1 A k B k exp(–λ k x), B k =1– a  π λ k  ln(4λ k )+C  , where C = 0.5772 is the Euler constant. 2.5. Equations Whose Kernels Contain Trigonometric Functions 2.5-1. Kernels Containing Cosine 1. y(x) ... y(x)+A  x a t k cosh m (λx)y(t) dt = f(x). This is a special case of equation 2.9.2 with g(x)=–A cosh m (λx) and h(t)=t k . 10. y(x)+A  x a x k cosh m (λt)y(t) dt = f...

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... dt. • Reference: S. G. Samko, A. A. Kilbas, and O. I. Marichev (1993). 1.9. Equations Whose Kernels Contain Arbitrary Functions 1.9-1. Equations With Degenerate Kernel: K(x, t)=g 1 (x)h 1 (t)+g 2 (x)h 2 (t) 1.  x a g(x)h(t)y(t) ... C, D, a, b, c, α, β, γ, λ, and µ are free parameters; and m and n are nonnegative integers. 2.1. Equations Whose Kernels Contain Power-Law Functions 2.1-1...

Ngày tải lên: 23/07/2014, 16:20

... Press LLC 10. 6. Dual Integral Equations of the First Kind 10. 6-1. The Carleman Method for Equations With Difference Kernels 10. 6-2. Exact Solutions of Some Dual Equations of the First Kind 10. 6-3. ... Kind 10. Methods for Solving Linear Equations of the Form  b a K(x, t)y(t) dt = f(x) 10. 1. Some Definition and Remarks 10. 1-1. Fredholm Integral Equations of the First Kin...

Ngày tải lên: 23/07/2014, 16:20