# Solving by substitution

When Solving by substitution, there are often multiple ways to approach it. We will give you answers to homework.

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In algebra, one of the most important concepts is Solving by substitution. The pressure based coupling algorithm solves the coupled equations including momentum equation and pressure based continuity equation. Therefore, in the coupling algorithm, steps 2 and 3 in the separation solution algorithm are replaced by a single step of solving the coupled equations. The other equations are solved by decoupling in the separation algorithm; Because the momentum and continuity equations are solved in a tightly coupled manner, the convergence speed of the solution is significantly improved compared with the separation algorithm. However, since all discrete systems based on momentum and pressure continuity equations must be stored in memory when solving the velocity field and pressure field (instead of storing only one equation like the separation algorithm), the storage requirement increases by 1.5-2 times as much as that of the separation algorithm.

In practical application, many problems are quite complex, and the differential equations constructed are also very complex. It is impossible to obtain the expression of y = f (x). Fortunately, many problems do not need to solve the expression, only need to calculate the value of Y. Since Newton, many mathematicians have studied the numerical solution of differential equations. Interpret neural networks as discrete schemes for solving differential equations? The field of numerical solution will pay attention to the numerical convergence of discrete schemes, but what is the connection between this and differential equations? How to map the input-output mapping of network connection to the infinite dimensional mapping of differential equations? Using the knowledge of dynamic systems to analyze the characteristics of neural networks? Many differential equations can be solved by direct integration, but some differential equations cannot.

Words and grammar can be carried out at the same time. It is not necessary to recite the words before reviewing the grammar. Memorizing words is to solve the problem that you can't understand words; Learning grammar is to solve the problem that you know all the words but can't make a sentence. Is there a way to memorize words, which can not only solve the problem of review planning to overcome forgetting, but also solve the problem of speed of memorizing words? I mainly recommend Liao Weiwei's sleep memory method here, because this method I eat very thoroughly, and it is also a free public welfare method.

Instead, he let the children understand the positions of both sides of the incident from the incident and taught them to solve the problems in their own way. The teacher is responsible for educating children, including some naughty children, mediating from them, and using experience to let both sides think about problems and better solve problems. However, whether we fully vent this emotion to our children or quickly focus on the problem itself and solve the problem quickly with appropriate methods is the embodiment of our childcare wisdom. We try to guide children to give solutions by themselves, which can better give us trust and the ability to solve problems. Learning is a heavy task and a long way to go.

Although the Ministry of education has been advocating that the creators of questions should focus on the teaching materials, the ever-changing mathematical problems, even a simple multiple-choice problem, can involve a lot of knowledge points. Therefore, candidates must not give up their confidence because of the difficulty of mathematics. Every year's college entrance examination mathematics will not be simple. Even if you can't solve this math problem yourself, you should have confidence in yourself, because there will be literature synthesis or science synthesis next.

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