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离散微分方程代码 已有1人参与
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clc,clear n=100; x1(1)=1; x2(1)=3; x3(1)=5; x4(1)=7; x5(1)=9; x6(1)=8; x7(1)=6; x8(1)=4; x9(1)=0.2; x10(1)=0.4; x11(1)=0.6; x12(1)=0.8; x13(1)=0.9; x14(1)=0.7; x15(1)=0.5; x16(1)=0.3; k(1)=0; for i=2:n; T=0.3; c=1; d=2; c1=1; x1(i)=x1(i-1)+T*x9(i-1)-c*T*T*(((x2(i-1)-x1(i-1))^2+(x6(i-1)-x5(i-1))^2-d^2)/((x2(i-1)-x1(i-1))^2+(x6(i-1)-x5(i-1))^2)^2)*x1(i-1)+c*T*T*(((x2(i-1)-x1(i-1))^2+(x6(i-1)-x5(i-1))^2-d^2)/((x2(i-1)-x1(i-1))^2+(x6(i-1)-x5(i-1))^2)^2)*x2(i-1)-1/2*T*T*c1*x9(i-1)+1/2*T*T*c1*x10(i-1); x2(i)=x2(i-1)+T*x10(i-1)-c*T*T*(((x3(i-1)-x2(i-1))^2+(x7(i-1)-x6(i-1))^2-d^2)/((x3(i-1)-x2(i-1))^2+(x7(i-1)-x6(i-1))^2)^2)*x2(i-1)+c*T*T*(((x3(i-1)-x2(i-1))^2+(x7(i-1)-x6(i-1))^2-d^2)/((x3(i-1)-x2(i-1))^2+(x7(i-1)-x6(i-1))^2)^2)*x3(i-1)-1/2*T*T*c1*x10(i-1)+1/2*T*T*c1*x11(i-1); x3(i)=x3(i-1)+T*x11(i-1)-c*T*T*(((x4(i-1)-x3(i-1))^2+(x8(i-1)-x7(i-1))^2-d^2)/((x4(i-1)-x3(i-1))^2+(x8(i-1)-x7(i-1))^2)^2)*x3(i-1)+c*T*T*(((x4(i-1)-x3(i-1))^2+(x8(i-1)-x7(i-1))^2-d^2)/((x4(i-1)-x3(i-1))^2+(x8(i-1)-x7(i-1))^2)^2)*x4(i-1)-1/2*T*T*c1*x11(i-1)+1/2*T*T*c1*x12(i-1); x4(i)=x4(i-1)+T*x12(i-1)-c*T*T*(((x1(i-1)-x4(i-1))^2+(x5(i-1)-x8(i-1))^2-d^2)/((x1(i-1)-x4(i-1))^2+(x5(i-1)-x8(i-1))^2)^2)*x4(i-1)+c*T*T*(((x1(i-1)-x4(i-1))^2+(x5(i-1)-x8(i-1))^2-d^2)/((x1(i-1)-x4(i-1))^2+(x5(i-1)-x8(i-1))^2)^2)*x1(i-1)-1/2*T*T*c1*x12(i-1)+1/2*T*T*c1*x9(i-1); x5(i)=x5(i-1)+T*x13(i-1)-c*T*T*(((x2(i-1)-x1(i-1))^2+(x6(i-1)-x5(i-1))^2-d^2)/((x2(i-1)-x1(i-1))^2+(x6(i-1)-x5(i-1))^2)^2)*x5(i-1)+c*T*T*(((x2(i-1)-x1(i-1))^2+(x6(i-1)-x5(i-1))^2-d^2)/((x2(i-1)-x1(i-1))^2+(x6(i-1)-x5(i-1))^2)^2)*x6(i-1)-1/2*T*T*c1*x13(i-1)+1/2*T*T*c1*x14(i-1); x6(i)=x6(i-1)+T*x14(i-1)-c*T*T*(((x3(i-1)-x2(i-1))^2+(x7(i-1)-x6(i-1))^2-d^2)/((x3(i-1)-x2(i-1))^2+(x7(i-1)-x6(i-1))^2)^2)*x6(i-1)+c*T*T*(((x3(i-1)-x2(i-1))^2+(x7(i-1)-x6(i-1))^2-d^2)/((x3(i-1)-x2(i-1))^2+(x7(i-1)-x6(i-1))^2)^2)*x7(i-1)-1/2*T*T*c1*x14(i-1)+1/2*T*T*c1*x15(i-1); x7(i)=x7(i-1)+T*x15(i-1)-c*T*T*(((x4(i-1)-x3(i-1))^2+(x8(i-1)-x7(i-1))^2-d^2)/((x4(i-1)-x3(i-1))^2+(x8(i-1)-x7(i-1))^2)^2)*x7(i-1)+c*T*T*(((x4(i-1)-x3(i-1))^2+(x8(i-1)-x7(i-1))^2-d^2)/((x4(i-1)-x3(i-1))^2+(x8(i-1)-x7(i-1))^2)^2)*x8(i-1)-1/2*T*T*c1*x15(i-1)+1/2*T*T*c1*x16(i-1); x8(i)=x8(i-1)+T*x16(i-1)-c*T*T*(((x1(i-1)-x4(i-1))^2+(x5(i-1)-x8(i-1))^2-d^2)/((x1(i-1)-x4(i-1))^2+(x5(i-1)-x8(i-1))^2)^2)*x8(i-1)+c*T*T*(((x1(i-1)-x4(i-1))^2+(x5(i-1)-x8(i-1))^2-d^2)/((x1(i-1)-x4(i-1))^2+(x5(i-1)-x8(i-1))^2)^2)*x5(i-1)-1/2*T*T*c1*x16(i-1)+1/2*T*T*c1*x13(i-1); x9(i)=x9(i-1)-2*T*c*(((x2(i-1)-x1(i-1))^2+(x6(i-1)-x5(i-1))^2-d^2)/((x2(i-1)-x1(i-1))^2+(x6(i-1)-x5(i-1))^2)^2)*x1(i-1)+2*c*T*(((x2(i-1)-x1(i-1))^2+(x6(i-1)-x5(i-1))^2-d^2)/((x2(i-1)-x1(i-1))^2+(x6(i-1)-x5(i-1))^2)^2)*x2(i-1)-T*c1*x9(i-1)+T*c1*x10(i-1); x10(i)=x10(i-1)-2*T*c*(((x3(i-1)-x2(i-1))^2+(x7(i-1)-x6(i-1))^2-d^2)/((x3(i-1)-x2(i-1))^2+(x7(i-1)-x6(i-1))^2)^2)*x2(i-1)+2*c*T*(((x3(i-1)-x2(i-1))^2+(x7(i-1)-x6(i-1))^2-d^2)/((x3(i-1)-x2(i-1))^2+(x7(i-1)-x6(i-1))^2)^2)*x3(i-1)-T*c1*x10(i-1)+T*c1*x11(i-1); x11(i)=x11(i-1)-2*T*c*(((x4(i-1)-x3(i-1))^2+(x8(i-1)-x7(i-1))^2-d^2)/((x4(i-1)-x3(i-1))^2+(x8(i-1)-x7(i-1))^2)^2)*x3(i-1)+2*c*T*(((x4(i-1)-x3(i-1))^2+(x8(i-1)-x7(i-1))^2-d^2)/((x4(i-1)-x3(i-1))^2+(x8(i-1)-x7(i-1))^2)^2)*x4(i-1)-T*c1*x11(i-1)+T*c1*x12(i-1); x12(i)=x12(i-1)-2*T*c*(((x1(i-1)-x4(i-1))^2+(x5(i-1)-x8(i-1))^2-d^2)/((x1(i-1)-x4(i-1))^2+(x5(i-1)-x8(i-1))^2)^2)*x4(i-1)+2*c*T*(((x1(i-1)-x4(i-1))^2+(x5(i-1)-x8(i-1))^2-d^2)/((x1(i-1)-x4(i-1))^2+(x5(i-1)-x8(i-1))^2)^2)*x1(i-1)-T*c1*x12(i-1)+T*c1*x9(i-1); x13(i)=x13(i-1)-2*T*c*(((x2(i-1)-x1(i-1))^2+(x6(i-1)-x5(i-1))^2-d^2)/((x2(i-1)-x1(i-1))^2+(x6(i-1)-x5(i-1))^2)^2)*x5(i-1)+2*c*T*(((x2(i-1)-x1(i-1))^2+(x6(i-1)-x5(i-1))^2-d^2)/((x2(i-1)-x1(i-1))^2+(x6(i-1)-x5(i-1))^2)^2)*x6(i-1)-T*c1*x13(i-1)+T*c1*x14(i-1); x14(i)=x14(i-1)-2*T*c*(((x3(i-1)-x2(i-1))^2+(x7(i-1)-x6(i-1))^2-d^2)/((x3(i-1)-x2(i-1))^2+(x7(i-1)-x6(i-1))^2)^2)*x6(i-1)+2*c*T*(((x3(i-1)-x2(i-1))^2+(x7(i-1)-x6(i-1))^2-d^2)/((x3(i-1)-x2(i-1))^2+(x7(i-1)-x6(i-1))^2)^2)*x7(i-1)-T*c1*x14(i-1)+T*c1*x15(i-1); x15(i)=x15(i-1)-2*T*c*(((x4(i-1)-x3(i-1))^2+(x8(i-1)-x7(i-1))^2-d^2)/((x4(i-1)-x3(i-1))^2+(x8(i-1)-x7(i-1))^2)^2)*x7(i-1)+2*c*T*(((x4(i-1)-x3(i-1))^2+(x8(i-1)-x7(i-1))^2-d^2)/((x4(i-1)-x3(i-1))^2+(x8(i-1)-x7(i-1))^2)^2)*x8(i-1)-T*c1*x15(i-1)+T*c1*x16(i-1); x16(i)=x16(i-1)-2*T*c*(((x1(i-1)-x4(i-1))^2+(x5(i-1)-x8(i-1))^2-d^2)/((x1(i-1)-x4(i-1))^2+(x5(i-1)-x8(i-1))^2)^2)*x8(i-1)+2*c*T*(((x1(i-1)-x4(i-1))^2+(x5(i-1)-x8(i-1))^2-d^2)/((x1(i-1)-x4(i-1))^2+(x5(i-1)-x8(i-1))^2)^2)*x5(i-1)-T*c1*x16(i-1)+T*c1*x13(i-1); k(i)=k(i-1)+1; end i=1:n; % plot(k,x9(  ,'g')% hold on; % plot(k,x10( ,'b')% plot(k,x11( ,'r')% plot(k,x12( ,'c')% xlabel('T-步') % ylabel('m/s-速度') % legend('自主体',1); plot(x1( ,x5(,'g')hold on; plot(x2( ,x6(,'b')plot(x3( ,x7(,'r')plot(x4( ,x8(,'c')xlabel('x轴位移') ylabel('y轴位移') legend('自主体',1); % plot(i-1,x13( ,'g')% hold on; % plot(i-1,x14( ,'b')% plot(i-1,x15( ,'r')% plot(i-1,x16( ,'c') |
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