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A_03 RUNGE KUTTA METHOD O(4)
PROGRAM EM IMPLICIT NONE REAL::T,Y,Z,H,F,K1,K2,K3,K4 INTEGER::I,N,INT PRINT*,'ENTER THE VALUE OF T:' READ*,T PRINT*,'ENTER THE VALUE OF Y:' READ*,Y PRINT*,'ENTER THE VALUE OF Y(T):' READ*,Z PRINT*,'ENTER THE VALUE OF STEP SIZE :' READ*,H N=INT((Z-T)/H) DO I = 1,N K1=H*F(T,Y) K2=H*F(T+H/2,Y+K1/2) K3=H*F(T+H/2,Y+K2/2) K4=H*F(T+H,Y+K3) Y=(K1+2*K2+2*K3+K4)/6+Y T=T+H PRINT*, I ,T ,Y END DO PRINT*,'THE ESTIMATE VALUE OF Y AT T IS:',Y END PROGRAM EM REAL FUNCTION F(T,Y) REAL::T,Y F=T**2.0-T*Y+Y**2.0 END FUNCTION F
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