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Handbook of mathematics for engineers and scienteists part 130

Handbook of mathematics for engineers and scienteists part 130. Tài liệu toán học quốc tế để phục vụ cho các bạn tham khảo, tài liệu bằng tiếng anh rất hữu ích cho mọi người. | References for Chapter 16 871 On applying the quadrature formula from Subsection 16.4.11 and neglecting the approximation error we transform relations 16.5.3.42 into the nonlinear system of algebraic or transcendental equations n Vi - AjKijy fi i 1 . n 16.5.3.43 for the approximate values yi of the solution y x at the nodes x1 . xn where fi f xi and Kij yj K xi tj yj and Aj are the coefficients of the quadrature formula. The solution of the nonlinear system 16.5.3.43 gives values y1 . yn for which by interpolation we find an approximate solution of the integral equation 16.5.3.41 on the entire interval a fi . For the analytic expression of an approximate solution we can take the function n y x f x 22 Aj K x xj yj . References for Chapter 16 Atkinson K. E. Numerical Solution of Integral Equations of the Second Kind Cambridge University Press Cambridge 1997. Bakhvalov N. S. Numerical Methods in Russian Nauka Publishers Moscow 1973. Bateman H. and Erdelyi A. Tables of Integral Transforms. Vols. 1 and 2 McGraw-Hill New York 1954. Bitsadze A.V. Integral Equation of the First Kind World Scientific Publishing Co. Singapore 1995. Brunner H. Collocation Methods for Volterra Integral and Related Functional Differential Equations Cambridge University Press Cambridge 2004. Cochran J. A. The Analysis of Linear Integral Equations McGraw-Hill New York 1972. Corduneanu C. Integral Equations and Applications Cambridge University Press Cambridge 1991. Courant R. and Hilbert D. Methods of Mathematical Physics. Vol. 1 Interscience New York 1953. Delves L. M. and Mohamed J. L. Computational Methods for Integral Equations Cambridge University Press Cambridge 1985. Demidovich B. P. Maron I. A. and Shuvalova E. Z. Numerical Methods. Approximation of Functions and Differential and Integral Equations in Russian Fizmatgiz Moscow 1963. Ditkin V. A. and Prudnikov A. P. Integral Transforms and Operational Calculus Pergamon Press New York 1965. Dzhuraev A. Methods of Singular Integral Equations