clc clear x=[0 0.2 0.4 0.6 0.8] h=0.2 y(1,1)=-1 for i=1:4 k1(1,i)=h*(-2*x(1,i)-y(1,i)) k2(1,i)=h*(-2*(x(1,i)+h/4)-(y(1,i)+k1(1,i)/4)) k3(1,i)=h*(-2*(x(1,i)+(3*h)/8)-(y(1,i)+(3*k1(1,i))/32+(9*k2(1,i))/32)) k4(1,i)=h*(-2*(x(1,i)+(12*h)/13)-(y(1,i)+(1932*k1(1,i))/2197-(7200*k2(1,i))/2197+(7296*k3(1,i))/2197)) k5(1,i)=h*(-2*(x(1,i)+(h))-(y(1,i)+(439*k1(1,i))/216-(8*k2(1,i))+(3680*k3(1,i))/513-(845*k4(1,i)/4104))) k6(1,i)=h*(-2*(x(1,i)+(h/2))-(y(1,i)-(8*k1(1,i))/27+(2*k2(1,i))-(3544*k3(1,i))/2565+(1859*k4(1,i)/4104)-11*k5(1,i)/40)) kA(1,i)=(16*k1(1,i)/135+6656*k3(1,i)/12825+28561*k4(1,i)/56430-9*k5(1,i)/50+2*k6(1,i)/55) y(1,i+1)=y(1,i)+kA(1,i) B(1,i)=-3.*exp(-x(1,i))-2*x(1,i)+2 C(1,i)=-2*x(1,i)-y(1,i) end for i=1:3 T=[x(1,i), y(1,i),B(1,i) ,C(1,i)] disp(T) end P=y(1,3)+(h/12)*(23*C(1,3)-16*C(1,2)+5*C(1,1)) printf('Value at y(0.6) is %f',P) x=[0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8] h=0.1 y(1,1)=-1 for i=1:7 k1(1,i)=h*(-2*x(1,i)-y(1,i)) k2(1,i)=h*(-2*(x(1,i)+h/4)-(y(1,i)+k1(1,i)/4)) k3(1,i)=h*(-2*(x(1,i)+(3*h)/8)-(y(1,i)+(3*k1(1,i))/32+(9*k2(1,i))/32)) k4(1,i)=h*(-2*(x(1,i)+(12*h)/13)-(y(1,i)+(1932*k1(1,i))/2197-(7200*k2(1,i))/2197+(7296*k3(1,i))/2197)) k5(1,i)=h*(-2*(x(1,i)+(h))-(y(1,i)+(439*k1(1,i))/216-(8*k2(1,i))+(3680*k3(1,i))/513-(845*k4(1,i)/4104))) k6(1,i)=h*(-2*(x(1,i)+(h/2))-(y(1,i)-(8*k1(1,i))/27+(2*k2(1,i))-(3544*k3(1,i))/2565+(1859*k4(1,i)/4104)-11*k5(1,i)/40)) kA(1,i)=(16*k1(1,i)/135+6656*k3(1,i)/12825+28561*k4(1,i)/56430-9*k5(1,i)/50+2*k6(1,i)/55) y(1,i+1)=y(1,i)+kA(1,i) B(1,i)=-3.*exp(-x(1,i))-2*x(1,i)+2 C(1,i)=-2*x(1,i)-y(1,i) end for i=1:6 T=[x(1,i), y(1,i),B(1,i) ,C(1,i)] disp(T) end R=y(1,6)+(h/12)*(23*C(1,6)-16*C(1,5)+5*C(1,4)) printf('Value at y(0.6) is %f',)