Variable step euler method for real-time simulation

Many systems have stiff characteristics. To simulate such system in real-time demands solver of differential equation having small fixed step size to guarantee stability and accuracy even if it may cost large number of computing resource. An adaptive variable minor step size Euler method is developed for real-time simulation. It alternately uses forward Euler and backward Euler method based on morbid degree. And then it divides fixed major step equally into multiple minor steps in according to local truncation error. Because of this, it is more precise and more robust than classic Euler method. While simulating large scale system, it realizes computing resource dynamic allocation in different sub-systems. The advantageous abilities are verified by typical real-time simulation problems and the usage in a flight simulator. These shows the method is very suitable for a long real-time simulation.