From top student in college to scientific research powerhouse

Chapter 5: Don't even mention you, I don't understand it either!
"Transformation, substitution, or direct discretization, until the computational load of computer simulation is greatly reduced."

The direction is very clear.

Zhang Minghao began his analysis seriously, his pen scribbling incessantly on the paper.

The entire page contained only one transformation of the equation and its discrete expression.

Yu Minxia, ​​sitting next to her, looked somewhat bewildered. She shook her head and said, "I don't think that will work."

"I've tried this solution, but it gets increasingly complicated later on..."

"Try it."

Zhang Minghao didn't even look up before switching to the next sheet of paper and moving on to the next step.

Next step, and the next step after that...

More than half an hour later, the table was covered with densely packed manuscript papers.

He paused briefly, then muttered to himself, "If I change it again, will it start to converge?"

Yu Minxia pursed her lips and added, "I think it will only get more complicated..."

"Watch!"

Zhang Minghao continued writing, using three pages to complete only one expression.

Then, continue.

Yu Minxia studied it carefully and found that some steps were not very clear, but as a doctoral student in mathematics specializing in partial differential equations, she could generally understand it.

She couldn't understand Zhang Minghao's thought process, so what was the point of constantly expanding her analysis?

She tried it, but it didn't work at all!
After looking at it for a long time, I rubbed my forehead, looked around, and then looked down again, but I couldn't keep up with the train of thought.

That's mathematics.

If you lose focus even for a moment, your train of thought may be interrupted.

After waiting for more than ten minutes, Zhang Minghao looked up, his face beaming with joy, and said, "You've really toned it down!"

"Really?" Yu Minxia didn't understand.

"Didn't you notice?" Zhang Minghao explained excitedly, "Some items can be merged or simplified, and some can be substituted with very similar values."

"After a few more transformations, the computational workload of the equation will be greatly reduced, even exponentially."

"Then it will be finished."

"what……"

Yu Minxia kept her mouth slightly open but couldn't say anything.

Should we continue with such complex transformations? Or should we simplify them? Or exponentially reduce the computational load?

impossible?

Zhang Minghao didn't offer any further explanation or analysis. He simply tidied up the large pile of papers on the table and handed them all to Yu Minxia, ​​saying, "They're all here. Take a look for yourself."

"I'll watch my own game."

"oh oh."

Yu Minxia took the manuscript paper, put it in her bag, and left with a bewildered expression.

Zhang Minghao stretched and yawned. He first went outside for a walk and rested for a while, then came back and began to study his equation problem.

I learned a lot just now.

When he did his research, he didn't think from a mathematical perspective at all; he just wanted to find a more approximate solution by 'transformation' and 'substituting values'.

This is the most common practice.

Yu Minxia's method helped broaden my thinking and find the general direction for solving the problem. The method should be applicable to the same type of equation.

However, the specifics have not yet been thoroughly studied.

Yu Minxia's equation problem has been solved, but it only solves one equation. Other equations still need to be analyzed again.

This involves a key element – ​​substitution transformation.

In the process of analyzing the equations, the method of 'approximate substitution transformation' was used many times. However, the 'approximate substitution transformation' method was not a conventional method, but rather a conclusion obtained directly through 'correct perception'.

That's the problem.

He can rely on 'correct perception' to complete the process of approximate simplification of equations.

Of course, no one else could do it.

Therefore, it is necessary to study several equations, find a large number of correct 'approximate substitution transformation' forms, and put them all together to find patterns.

Use the results to deduce the principles and processes.

"It's a bit complicated, but I think it should be okay?" Zhang Minghao pondered and began to study it carefully.

……

Meanwhile, Yu Minxia returned to her residence in a daze.

She had a bad feeling about it. Even when she got to the door, she still couldn't understand why she had taken the things and left.

The original plan was to spend an afternoon in the study room and study it carefully.

Upon entering, I saw Li Li on the sofa.

Yu Minxia suddenly found a reason. She took out a stack of manuscript paper covered with symbols from her bag and handed it over eagerly. "Guess who I ran into today!"

Li Li took the manuscript paper, glanced at it, and then put it back on the table, saying numbly, "Do you think someone like me, a law student, can understand this?"

"I'm asking you to guess who I ran into!"

"You seem so excited, did you run into a handsome guy? Or a celebrity? Or maybe a freshman? Didn't you say last time that there was a really good-looking freshman..."

"What are you talking about!"

Yu Minxia rolled her eyes in exasperation. "I ran into Zhang Minghao!"

"Zhang Minghao?"

"The guy who rented the room yesterday, you don't have to worry about him this time. He's definitely a PhD. Look at these, how could anyone but a math PhD write this!"

"Take a closer look, the direct transformation of partial differential equations is discretization..."

Li Li pressed her forehead hard and quickly interrupted, "Stop, stop, stop! Stop!"

"Also, he said he's in the physics department, a doctoral student who's about to start, right? A year younger than you!"

"Forehead……"

Yu Minxia paused for a moment, then suddenly realized what was strange.

A physics PhD student about to enroll is teaching a math PhD student a year ahead of her to analyze partial differential equations.
So outrageous?
Furthermore, there were parts of the other party's analysis that I didn't even understand.

She suddenly became somewhat withdrawn, let out a long sigh, and said nothing more. Instead, she picked up the stack of manuscript papers and began to examine them carefully.

I followed the train of thought for the first part, but there are still some parts I don't understand.

She studied it patiently, but found that she still couldn't understand the parts she hadn't understood before.

"How can you just empathize like that?"

"why?"

"How was it calculated? But the verification result is correct..."

Yu Minxia found herself unable to understand. She scratched her head, trying to figure it out, but she couldn't understand it at all; she hadn't even fully grasped the first transformation.

"No! We must figure this out!"

Forget about research, she, a PhD student in mathematics, couldn't understand the mathematical analysis done by a junior physics student about to enter university.
Ok!

Even if you don't understand it, you still have to figure it out, even if it proves you wrong!
It's normal not to understand something that's wrong.

Yu Minxia became increasingly depressed. She put the manuscript paper into her bag, picked up the bag, and went out again.

She went to the Science Building and found her advisor, Meng Guoqing.

Meng Guoqing was a middle-aged man nearing fifty, with a receding hairline and thick glasses, giving him the typical air of an old professor.

He stared at the manuscript for a long time before asking, "He said that if we continue to substitute and transform, the equation will eventually converge, and the computational workload will be greatly reduced?"

"Correct."

Yu Minxia nodded.

"Overall, that's the case," Meng Guoqing explained the conclusion. "Upon analyzing the last part, the equation does indeed show a tendency to converge."

"I understand this."

Yu Minxia nodded, pointing to a spot on the second page. "It's mainly here. There are several more later on. Each overall change is reflected here. How is it incorporated?"

"Why is it in this form? Where did it come from? Why? I don't understand it at all."

"I checked the calculation, and the result is fine."

Meng Guoqing stared at that spot carefully, and then simply took out a pen to verify the calculations.

After some calculations, I put down my pen.

He adjusted his glasses, raised his head, pursed his lips, and pondered for a long time before finally saying, "This transformation is indeed correct, but... don't say you don't understand it, I don't understand it either."

"Let's put this here for now, I'll take a closer look..."

"By the way, who made it?"

Yu Minxia replied, "Zhang Minghao, a doctoral student in the Physics Department, I think he enrolled in March."

"Physics Department? Not enrolled yet?"

"Correct."

Meng Guoqing opened his mouth, thought for a moment, and then nodded. "You go first, I'll take another look."

(End of this chapter)