MATLAB实现特殊函数计算，案例丰富【数学建模、科学计算算法】.zip

function Jx = bessel(n,x) format long; if n == 0 a = [5.7568490574e10;-1.3362590354e10;6.516196407e8; -1.121442418e7;7.739233017e4;-1.849052456e2]; b = [5.7568490411e10;1.029532985e9;9.494680718e6; 5.927264853e4;2.678532712e2;1.0]; r =[1.0;-0.1098628627e-2;0.2734510407e-4; -0.2073370639e-5;0.2093887211e-6]; s =[-0.1562499995e-1;0.1430488765e-3;-0.6911147651e-5; 0.7621095161e-6;-0.934945152e-7]; if abs(x) < 8 J0_u = a(1); J0_d = b(1); for i=2:6 J0_u = J0_u + a(i)*power(x,2*(i-1)); J0_d = J0_d + b(i)*power(x,2*(i-1)); end J0 = J0_u/J0_d; else z = 8/abs(x); sita = abs(x) - pi/4; R0 = r(1); S0 = s(1); for i=2:5 R0 = R0 + r(i)*power(z,2*(i-1)); S0 = S0 + s(i)*power(z,2*(i-1)); end J0 = (R0*cos(sita)-z*S0*sin(sita))*sqrt(2/pi/abs(x)); end Jx = J0; else if n == 1 c = [7.2362614232e10;-7.895059235e9;2.423968531e8; -2.972611439e6;1.570448260e4;-3.016036606e1]; d = [1.44725228443e11;2.300535178e9;1.858330474e7; 9.944743994e4;3.769991397e2;1.0]; p = [1.0;0.183105e-2;-0.3516396496e-4; 0.2457520174e-5;-0.240337019e-6]; q = [0.4687499995e-1;-0.2002690873e-3; 0.8449199096e-5;-0.88228987e-6; 0.105787412e-6]; if abs(x) < 8 J1_u = c(1); J1_d = d(1); for i=2:6 J1_u = J1_u + c(i)*power(x,2*(i-1)); J1_d = J1_d + d(i)*power(x,2*(i-1)); end J1 = x*J1_u/J1_d; else z = 8/abs(x); fi = abs(x) - 3*pi/4; P1 = p(1); Q1 = q(1); for i=2:5 P1 = P1 + p(i)*power(z,2*(i-1)); Q1 = Q1 + q(i)*power(z,2*(i-1)); end J1 = (P1*cos(fi)-z*Q1*sin(fi))*sqrt(2/pi/abs(x)); if x<0 J1 = -J1; end end Jx = J1; else if abs(x) > n y = 2/x; bess1 = bessel(0,x); bess2 = bessel(1,x); for j=1:n-1 Jx = j*y*bess2 - bess1; bess1 = bess2; bess2 = Jx; end else M = 2*floor(((n + floor(sqrt(40*n))))/2); JS = zeros(M+2 ,1); JS(M+2) = 0; JS(M+1) = 1; y = 2/x; bSum = 0; for k=M:-1:1 JS(k) = JS(k+1)*y*k - JS(k+2); end BK = JS(1); for k=1:floor(M/2) BK = BK + 2*JS(2*k+1); end Jx = JS(n+1)/BK; end end end