What is a system of difference equations and what does difference equation mean

The square of the difference equation y is 2 1=2 +2a+b+1 =73 (-2)=3 +3a-2b+(-2) =23.

It is widely used in problem solving, and the punch wheel involves the value range of the solution coefficient, the number and distribution of the root of the equation, and the pure condition of the judgment. The discriminant formula for the root of the unary quadratic equation ax 2+bx+c=0(a≠0) is b 2-4ac, denoted by " " (pronounced "delta").

Difference equation: Let it be a real sequence if the following relationship ut-1ut-1 -... is satisfied-put-p=h(t), where 1, 2...., p is the real number and h(t) is the known real function of t, then the above equation is called the linear difference equation satisfied.

If the deterministic function ut,h (t) in the above equation is replaced by a random sequence with known statistical properties, then the linear random difference equation is obtained. Such a wide range of models are not discussed in time series analysis.

xt-ᵠ1xt-1-…-pxt-p=εt-θ1εt-1-…-q t-g where 1, ....p, and 1, ....g is a real number, is a zero-mean stationary series, is a stationary white noise sequence, and when s>t, e sxt=0, the specific linear random difference equation mentioned above is the arma (p,g) model in time series analysis.

The square of the difference equation y is 2 1=2 +2a+b+1 =73 (-2)=3 +3a-2b+(-2) =23.

It is widely used in solving problems, involving the range of value of the solution coefficient, the number and distribution of the number of equation roots, etc. The discriminant formula for the root of the quadratic equation ax 2+bx+c=0(a≠0) is b 2-4ac, denoted by " " (pronounced "delta").

Theorem. 1. If y1 (t) and y2 (t) ,...ym(t) is the homogeneous linear difference equation yt+n+a1yt+n-1 +a2yt+n-2+....m special solutions (m2) of +an-1yt+1+anyt=0, then its linear combination y(t)=a1y1(t)+a2y2(t)+....amym(t) is also the solution of the equation known where, where a1, a2 ,..., am is an arbitrary constant.

2. Homogeneous linear difference equation of order nth order yt+n+a1yt+n-1 +a2yt+n-2 +....an-1yt+1+anyt=0 must have n linearly independent special solutions.

Difference equations are discretizations of differential equations.

Differential Equations] Differential equations are equations that describe the relationship between the derivatives of an unknown function and the independent variables. The solution of a differential equation is a function that conforms to the equation. In elementary mathematics, the solution of an algebraic equation is a constant value.

Differential equations have a wide range of applications and can be used to solve many derivative-related problems. Many kinematic and dynamic problems involving variable forces in physics, such as the falling motion of the air as a function of velocity, can be solved by differential equations. In addition to this hailstorm, differential equations have applications in fields such as chemistry, engineering, economics, and demography.

The study of differential equations in the field of mathematics focuses on several different aspects, but most are concerned with the solution of differential equations. There are only a few simple differential equations that can be solved analytically. However, even if the analytic solution is not found, it is still possible to confirm the partial nature of the solution.

When the analytical solution cannot be obtained, the numerical solution can be found by using a computer by means of numerical analysis. Dynamical system theory emphasizes the quantitative analysis of differential equation systems, while many numerical methods can calculate the numerical solutions of differential equations with a certain degree of accuracy.

Difference Equations] Difference equations, also known as recursive relations, are equations that contain unknown functions and their differences, but do not contain derivatives. The function that satisfies this equation is called the solution of the difference equation. Difference equations are discretizations of differential equations.

Mathematically, a recurrence relation, also known as a difference equation, is an equation that recursively defines a sequence: each item of the sequence is a function of the previous term. Some simply defined recursive relations can exhibit very complex (chaotic) properties, and they belong to the field of nonlinear analysis in mathematics.

The so-called solution of a recursive relation, that is, the analytical solution of it, that is, a non-recursive function with respect to n.

Difference equations are discretizations of differential equations. A differential equation can be solved exactly, but if it is a difference equation, an approximate solution can be found.

For example, dy+y*dx=0,y(0)=1 is a differential equation with x taking the value [0,1].

Note: The solution is y(x)=e (-x));

To discretize a differential equation, the interval of x can be divided into many small intervals [0,1 n],[1 n,2 n],n-1)/n,1]

In this way, the above differential equation can be discretized as:

Difference equations. y((k+1) n)-y(k n)+y(k shirt spring n)*(1 n)=0,k=0,1,2,..n-1 (n systems of discrete equations).

Using the condition of y(0)=1, we can calculate the approximate value of y(k n) using the forest group and the difference equation above.