1), Solve Equation (2.2) exactly for X 1 ( t + Δ t ) = Φ ( t , X ( t ) ) ;
2), Approximate numerically the equation (2.3)
For X 2 ( t + Δ t ) with initial condition
X 2 = X 1 ( t + Δ t ) , then
X 2 ( t + Δ t ) = X 1 ( t + Δ t ) + α ( X 1 ( t + Δ t ) , t ) Δ t + ⋯
3) Take X ( t + Δ t ) = X 2 ( t + Δ t ) . Thus
X ( t + Δ t ) = Φ ( t + Δ t , X ( t ) ) + α ( Φ ( t + Δ t , X ( t ) ) , t ) Δ t + ⋯