Mathematically, the difference method is a numerical method of differential equation, which approximates the derivative through finite difference, so as to find the approximate solution of differential equation.
"Difference method" is a quick calculation method when comparing the sizes of two fractions, and it is difficult to solve it by other quick calculation methods such as "direct division" or "identical method". It is an advanced skill based on high school mathematics and applied to data analysis and rapid calculation of public examinations.
Difference method is an approximate numerical solution of differential equation. Specifically, the difference method is to replace differential with finite difference and derivative with finite difference quotient, so that the basic equation and boundary conditions are approximately expressed by difference equations, and the problem of solving differential equations is transformed into the problem of solving algebraic equations. In elasticity, difference method and variational method are used to solve plane problems.
The error of approximate solution is defined as the difference between approximate solution and analytical solution. The two sources of errors in finite difference method are rounding error and truncation error (or discretization error). The former is caused by rounding error when the computer calculates decimals, and the latter is caused by the limitation of digital digits in the computer.
Pay special attention to
First, the "difference method" itself is an "accurate algorithm" rather than an "estimation method", and the obtained size relationship is accurate rather than rough.
Second, "difference method" and "similarity method" are often used together, and "difference method after similarity method" and "difference method after similarity method" are two situations that are often encountered in data analysis and rapid calculation.
Thirdly, direct division is often needed when comparing the difference score obtained by the difference method with the small score.
Fourth, if the two scores are very close, we even need to use the "difference method" twice, which is relatively complicated, but if it is skillfully used, it can greatly simplify the calculation.