1, with different definitions: differential equation refers to the equation describing the relationship between the derivative of unknown function and independent variables; Difference equation, also known as recursive relation, is an equation with unknown function and its difference, but no derivative.

2. The solution is not exactly the same: the solution of differential equation is a function that conforms to the equation, and in the algebraic equation of elementary mathematics, the solution is a constant value; The solution of the difference equation is a function that satisfies the equation, that is, an analytical solution.

3, the application is not exactly the same: the application of differential equations can solve many problems related to derivatives. Many kinematics and dynamics problems involving variable forces in physics can be solved by differential equations, which have applications in chemistry, engineering, economics and demography. Difference equations are often used in model applications.

Second, the difference equation is the discretization of the differential equation.

Extended data

The research on differential equations in the field of mathematics focuses on several different aspects, but most of them are related to the solutions of differential equations. Only a few simple differential equations can be solved analytically. However, even if the analytical solution is not found, some properties of the solution can still be confirmed. It is widely used and can solve many problems related to derivatives.

The common constraint condition of ordinary differential equations is the value of a function at a specific point. If it is a higher-order differential equation, the values of its derivatives will add up. Ordinary differential equations with this constraint are called initial value problems. If it is a second-order ordinary differential equation, it is also possible to specify the value of the function at two specific points, and the problem at this time is the boundary value problem; The common problems of partial differential equations are mainly boundary value problems, and the boundary condition is to specify the value or derivative of a specific hypersurface with specific conditions.

The difference equation is an equation that recursively defines a sequence: each term of the sequence is a function defined as the previous term. Some simple recursive relations may show very complex properties and belong to the field of nonlinear analysis in mathematics. Solve a recursive relation, that is, find its analytical solution, that is, the non-recursive function about n.

References:

Baidu encyclopedia-differential equation

References:

Baidu encyclopedia-difference equation