for ( i = 2 ; i < n-2 ; i++) { k1[i] = (- p*h[i]*(h[i+1]-h[i-1])/2 + nu * (h[i+1]-2*h[i]+h[i-1]) - a*(h[i+2]-2*h[i+1]+ 2*h[i-1]-h[i-2])/2)*dt; } for ( i = 4 ; i < n-4 ; i++) { k2[i] = (- p*(h[i]+ 0.5*k1[i])*(h[i+1] + 0.5*k1[i+1] -h[i-1] - 0.5*k1[i-1])/2 + nu * (h[i+1]+ 0.5*k1[i+1] -2*(h[i] + 0.5*k1[i]) + h[i-1] + 0.5*k1[i-1]) - a*(h[i+2] + 0.5*k1[i+2] -2*(h[i+1] + 0.5*k1[i+1])+ 2*(h[i-1] + 0.5*k1[i-1])-(h[i-2] + 0.5*k1[i-2]))/2)*dt; } for ( i = 6 ; i < n-6 ; i++) { k3[i] = (- p*(h[i]+ 0.5*k2[i])*(h[i+1] + 0.5*k2[i+1] -h[i-1] - 0.5*k2[i-1])/2 + nu * (h[i+1]+ 0.5*k2[i+1] -2*(h[i] + 0.5*k2[i]) + h[i-1] + 0.5*k2[i-1]) - a*(h[i+2] + 0.5*k2[i+2] -2*(h[i+1] + 0.5*k2[i+1])+ 2*(h[i-1] + 0.5*k2[i-1])-(h[i-2] + 0.5*k2[i-2]))/2)*dt; } for ( i = 8 ; i < n-8 ; i++) { k4[i] = (- p*(h[i]+ k3[i])*(h[i+1] + k3[i+1] -h[i-1] - k3[i-1])/2 + nu * (h[i+1]+ k3[i+1] -2*(h[i] + k3[i]) + h[i-1] + k3[i-1]) - a*(h[i+2] + k3[i+2] -2*(h[i+1] + k3[i+1])+ 2*(h[i-1] + k3[i-1])-(h[i-2] + k3[i-2]))/2)*dt; } for ( i = 8 ; i < n - 8 ; i++) { ho[i] = h[i] + (1/6)*(k1[i] + 2*k2[i] + 2*k3[i] + k4[i]); } for ( i = 8 ; i < n -8 ; i++) { h[i] = ho[i] ; }