Реферат: Численный расчет дифференциальных уравнений

2).x₂ =0,4; x_1+1/2 =x₁ +h/2=0,3

f₁₁ =a₁ =1,18 y_1+1/2 =1,22+1,18*0,1=1.338

f₂₁ =b₁ =0,78 a_1+1/2 =1,18+0,78*0,1=1,258

f₃₁ =2*0,2-1,22-1,18+0,78=-1,22 b_1+1/2 =-1,22*0,1+0,78=0,658

α₁ =a_1+1/2 =1,258 y₂ =1,22+1,258*0,2=1,4716

β₁ =b_1+1/2 =0,658 a₂ =1,18+0,658*0,2=1,3116

γ₁ =2*0,3-1,338-1,258+0,658=-1,338 b₂ =0,78-1,338*0,2=0,5124

3).x₃ =0,6; x_2+1/2 =0,5

f₁₂ =a₂ =1,3116 y_2+1/2 =1,47+1,3*0,1=1,60276

f₂₂ =b₂ =0,5124 a_2+1/2 =1,3116+0,5*0,1=1.36284

f₃₂ =2*0,4-1,47-1,31+0,512=-1,4708 b_2+1/2 =0,4-1,4*0,1=0,36542

α₂ =1,36284 y₃ =1,4716+1,3116*0,2=1,744168

β₂ =0,36542 a₃ =1,3116+0,3654*0,2=1,384664

γ₂ =2*0,5-1,6-1,36+0,365=-1,60018 b₃ = 0,51-1,60018*0,2=0,192364

4).x₄ =0,8; x_3+1/2 =0,7

f₁₃ =1,384664 y_3+1/2 =1,74+1,38*0,1=1,8826364

f₂₃ =0,192364 a_3+1/2 =1,38+0,19*0,1=1,4039204

f₃₃ =2*0,6-1,7-1,38+0,19=-1,736488 b_3+1/2 =0,19-1,7*0,1=0,0187152

α₃ =1,4039204 y₄ =1,74+1,4*0,2=2,0249477

β₃ =0,0187152 a₄ =1,38+0,9187*0,2=1,388403

γ₃ =2*0,7-1,88-1,4+0,0187=-1,8678416 b₄ =0,192-1,87*0,2=-0,1812235

5).x₄ =1; x_4+1/2 =0,9

f₁₄ =1,388403 y_4+1/2 =2,02+1,388*0,1=2,16379478

f₂₄ =-0,1812235 a_4+1/2 =1,4-0.181*0,1=1,370306608

f₃₄ =2*0,8-2,02-1,388-0,18=-1,9945834 b_4+1/2 =-0,18-1,99*0,1=-0,38066266

α₄ =1,3703 y₅ =2,02+1,37*0,2=2,2990038

β₄ =-0,38066 a₅ =1,388-0,38*0,2=1,3122669

γ₄ =2*0,9-2,16-1,37-0,38=-2,114764056 b₅ =-0,181-2,1*0,2=-0,6041734

Программа на Turbo Pascal

uses crt,pram,kurs1_1;