(D13) CSM$USERS:[WHEREMAN.PROGRAMS.NPAINLEVE.SINGLE]P_FISHER.OUT;2 (C14) batch("np_exec.max")$ (C15) /* ************************************************************************* */ /* Batch file NP_EXEC.MAX */ /* ************************************************************************* */ exec_painleve (eq, alpha, do_resonances, max_resonance, do_simplification)$ SUBSTITUTE X ----> G + X0 ---------------------------------------------------------------- 2 PAINLEVE ANALYSIS OF EQUATION, F + C F - F + F = 0 G G G ---------------------------------------------------------------- ALPHA SUBSTITUTE U G FOR f IN ORIGINAL EQUATION. 0 MINIMUM POWERS OF g ARE [2 ALPHA, ALPHA - 2] 2 ALPHA 2 * COEFFICIENT OF G IS - U 0 ALPHA - 2 * COEFFICIENT OF G IS U (ALPHA - 1) ALPHA 0 NOTE : THIS TERM VANISHES FOR [ALPHA = 0, ALPHA = 1] , VERIFY IF ANY OF THESE VALUES FOR ALPHA LEADS TO DOMINANT BEHAVIOR, IF IT DOES THEN RUN THE PROGRAM AGAIN WITH THIS VALUE AS USER SUPPLIED ALPHA, CALLED BETA. ---------------------------------------------------------------- FOR EXPONENTS ( 2 ALPHA ) AND ( ALPHA - 2 ) OF g, WITH alpha = - 2 , POWER OF g is - 4 ----> SOLVE FOR U 0 1 TERM - (U - 6) U -- IS DOMINANT 0 0 4 G IN EQUATION. ---------------------------------------------------------------- 1 ) WITH U = 6 ----> FIND RESONANCES 0 ALPHA R + ALPHA SUBSTITUTE U G + U G FOR f IN EQUATION 0 R R - 4 TERM ( (R - 6) (R + 1) ) U G IS DOMINANT R IN EQUATION. THE ONLY NON-NEGATIVE INTEGRAL ROOT IS [R = 6] WITH MAXIMUM RESONANCE = 6 ----> CHECK RESONANCES. 6 ==== \ K - 2 SUBSTITUTE POWER SERIES > U G FOR f IN EQUATION. / K ==== K = 0 WITH U = 6 0 1 * COEFFICIENT OF -- IS - 2 (6 C + 5 U ) 3 1 G 6 C U = - --- 1 5 2 6 (C + 50 U - 25) 1 2 * COEFFICIENT OF -- IS - ------------------- 2 25 G (C - 5) (C + 5) U = - --------------- 2 50 3 6 (C + 250 U ) 1 3 * COEFFICIENT OF - IS - --------------- G 125 3 C U = - --- 3 250 4 7 C + 5000 U - 125 4 * COEFFICIENT OF 1 IS - -------------------- 500 4 7 C - 125 U = - ---------- 4 5000 5 79 C - 1375 C + 75000 U 5 * COEFFICIENT OF G IS - ------------------------- 12500 4 C (79 C - 1375) U = - ---------------- 5 75000 2 2 2 2 C (6 C - 25) (6 C + 25) * COEFFICIENT OF G IS - -------------------------- 6250 U IS ARBITRARY ? 6 2 2 2 C (6 C - 25) (6 C + 25) COMPATIBILITY CONDITION: - -------------------------- = 0, 6250 *** CONDITION IS NOT SATISFIED. *** *** CHECK FOR FREE PARAMETERS OR PRESENCE OF U . *** 0 ---------------------------------------------------------------- (C16) output()$ ---------------------------------------------------------------- AT THE END OF THE COMPUTATIONS THE FOLLOWING ARE AVAILABLE: * U VALUE(S) (type uval[j,k,l] where 1 <= j <= 1 and 0 <= k <= [6] and 1 <= l <= [1] ) j stands for j_th alpha,k stands for u[k],l stands for l_th solution set for u[0] * ALPHA VALUE(S) (type alpha[j] where 1 <= j <= 1 ) j stands for j_th alpha * COMPATIBILITY CONDITION(S) (type compcond[j,k] where 1 <= j <= 1 and 1 <= k <= [1] ) j stands for j_th alpha,k stands for k_th solution set for u[0] * RESONANCE(S) (type res[j,k] where 1 <= j <= 1 and 1 <= k <= [1] ) j stands for j_th alpha,k stands for k_th solution set for u[0] ---------------------------------------------------------------- TO SEE THIS MENU AGAIN JUST TYPE < output() > ---------------------------------------------------------------- (C17) /* ************************** END of NP_EXEC.MAX ************************** */ (C18) closefile();