Tham khảo tài liệu 'mixed boundary value problems episode 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 168 Mixed Boundary Value Problems for j 1 N xx j dx xxi j dx end the value of x at the interfaces for j 0 N xx_e j 1 j dx xxi_e j 1 j dx end Solve the integral equation Equation for n 1 N x xx n b n x the right side of Equation for m 1 N xi xxi m if n m the first term on the left side of Equation AA n m h else AA n m 0 end if n m NN n m log sqrt 1-x x else NN n m log x-xi x sqrt 1-xi xi -xi sqrt 1-x x end NN n m NN n m log x xi Find the non-singular contribution from the integrals in Equation AA n m AA n m 2 NN n m dx pi . 2 asin x xi dx pi sqrt 1-xi xi end end Add in the contribution from the singular term for n 1 N for m 2 N k n-m 1 psi_0 -1 psi 1 k k- k-1 k-1 if k 0 psi_0 psi_0 k log abs k psi_1 psi_1 - k k log abs k end if k 1 psi_0 psi_0 - k-1 log abs k-1 2008 by Taylor Francis Group LLC Transform Methods 169 psi 1 psi 1 k-1 k-1 log abs k-1 end psi_1 psi_1 k psi_0 alpha dx log dx dx psi_0-psi_1 beta dx log dx dx psi_1 AA n m-1 AA n m-1 - alpha pi AA n m AA n m - beta pi end end f AA b Compute f x from Equation Having found f x from Equation g t follows from Equation . g 1 0 for n 2 N 1 t xx_e n g n 0 for m 1 n-1 xi xxi m g n g n 2 xi f m dx pi sqrt t t-xi xi end end With g t we can compute A k and u x y . The maximum number of wavenumbers included in the computations is K_max dk. The MATLAB code is Compute A k from Equation . Use Simpson s rule. for n 1 N derivative n g n 1 -g n dx end for k 0 K_max ak k dk t xx 1 A k 1 derivative 1 besselj 0 ak t k 0 term for n 2 N-1 t xx n if mod n 2 0 A k 1 A k 1 4 derivative n besselj 0 ak t else A k 1 A k 1 2 derivative n besselj 0 ak t end end t xx N k kmax term A k 1 A k 1 derivative N besselj 0 ak t A k 1 A k 1 dx 3 2008 by Taylor Francis Group LLC 170 Mixed Boundary Value Problems Figure The solution to Equation subject to the mixed boundary conditions given by Equation through Equation when h 1. end .
