share/contrib/diffequations/tests/rtestode_utils.mac

   1 (load("contrib_ode"),0);
   2 0$
   3
   4 /* Test cases for contrib_ode utility functions */
   5
   6 (load('contrib_ode), done);
   7 done;
   8
   9 bessel_simplify(4*bessel_j(n,x^2)*(x^2-n^2/x^2)
  10   +x*((bessel_j(n-2,x^2)-bessel_j(n,x^2))*x
  11   -(bessel_j(n,x^2)-bessel_j(n+2,x^2))*x)
  12   -2*bessel_j(n+1,x^2)+2*bessel_j(n-1,x^2));
  13 0;
  14
  15 bessel_simplify(((bessel_y(n-2,sqrt(x))-bessel_y(n,sqrt(x)))/(4*sqrt(x))
  16  -(bessel_y(n,sqrt(x))-bessel_y(n+2,sqrt(x)))/(4*sqrt(x)))
  17  /(4*sqrt(x))
  18  +bessel_y(n,sqrt(x))*(1-n^2/x)/(4*x)
  19  +(bessel_y(n-1,sqrt(x))-bessel_y(n+1,sqrt(x)))/(8*x^(3/2)));
  20 0;
  21
  22 bessel_simplify(-(bessel_k(1,x)*%c-bessel_i(1,x))^2*x^2/(bessel_k(0,x)*%c+bessel_i(0,x))^2
  23  +x^2
  24  +x*((-(bessel_k(2,x)+bessel_k(0,x))*%c/2-(bessel_i(2,x)+bessel_i(0,x))/2)*x
  25     /(bessel_k(0,x)*%c+bessel_i(0,x))
  26     -(bessel_i(1,x)-bessel_k(1,x)*%c)*(bessel_k(1,x)*%c-bessel_i(1,x))*x
  27      /(bessel_k(0,x)*%c+bessel_i(0,x))^2
  28     +(bessel_k(1,x)*%c-bessel_i(1,x))/(bessel_k(0,x)*%c+bessel_i(0,x))));
  29 0;
  30
  31 /* Check Struve H recurrence - integral of bessel_j(2,z)*z^2 dz */
  32 bessel_simplify(diff(3*%pi*(struve_h(1,z)*bessel_j(2,z)-bessel_j(1,z)*struve_h(2,z))*z/2,z)-bessel_j(2,z)*z^2);
  33 0;
  34
  35 /* Check Struve L recurrence - integral of z^v*struve_l(v-1,z) dz DLMF 11.7.3 */
  36 bessel_simplify(diff(z^v*struve_l(v,z),z)-z^v*struve_l(v-1,z));
  37 0;
  38
  39 expintegral_e_simplify(
  40  (%e^(2*x+2)+(%e*expintegral_e(1,-x-1)*x-%e*expintegral_e(2,-x-1)
  41  +%e*expintegral_e(1,-x-1))*%e^x)
  42  /(%e^2*%c^2*x^2+(2*%e^2*%c^2-2*%e*expintegral_e(2,-x-1)*%c)*x+%e^2*%c^2
  43    -2*%e*expintegral_e(2,-x-1)*%c+expintegral_e(2,-x-1)^2));
  44 0;
  45
  46 expintegral_e_simplify(
  47  -((2*expintegral_e(1/4,(2*x-1)/4)-2*expintegral_e(-3/4,(2*x-1)/4))*x*(2*x-1)^(3/4)*%e^((4*x-1)/4)+(expintegral_e(5/4,(2*x-1)/4)+2*expintegral_e(1/4,(2*x-1)/4)+expintegral_e(-3/4,(2*x-1)/4))*(2*x-1)^(3/4)*%e^((4*x-1)/4))/(8*x-4));
  48 0;
  49
  50 expintegral_e_simplify(
  51 %e^(-x-2)*(2*%e^(2*x+2)+(4*expintegral_e(2,-2*(x+1))-4*expintegral_e(1,-2*(x+1)))*x^2+(6*expintegral_e(2,-2*(x+1))-4*expintegral_e(3,-2*(x+1)))*x-2*expintegral_e(2,-2*(x+1))+4*expintegral_e(1,-2*(x+1))));
  52 0;
  53
  54 expintegral_e_simplify(
  55 -%e^(-3*x-5)*(x*((100*expintegral_e(2,5*(x-1))+300*expintegral_e(1,5*(x-1)))*%e^(5*x)-100*%e^5)+500*expintegral_e(1,5*(x-1))*x^2*%e^(5*x)+(160*expintegral_e(2,5*(x-1))-800*expintegral_e(1,5*(x-1)))*%e^(5*x)-160*%e^5));
  56 0;
  57
  58 /* verify that ode1_lie doesn't trigger an error on this problem.
  59  * contrib_ode doesn't appear to be able to solve it, which is OK, I guess.
  60  */
  61 block ([foo],
  62  declare (n, integer),
  63  foo : contrib_ode ('diff(x, t)^2 = alpha - beta*abs(x)^n, x, t),
  64  remove (n, integer),
  65  foo);
  66 false;
  67
  68 /* Allow subscripted variables in ode_check */
  69 ode_check('diff(y[2],x[1]),y[2]=%c);
  70 0;
  71
  72 ode_check('diff(x[2],x[1],2)-x[2],x[2]=%e^-x[1]*%k2+%e^x[1]*%k1);
  73 0;