D'Lembert Method for Solving the Wave Equation with Boundary Conditions

In summary, the D'Lembert method application is a mathematical technique used to estimate the mean of a population based on a sample. It works by calculating the sum of squared differences and is best used for small sample sizes and normally distributed populations. However, it has limitations and may not be accurate with skewed data. It differs from other statistical methods in that it is specifically used for estimation, rather than testing relationships or making predictions.
  • #1
Markov2
149
0
Solve

$\begin{aligned} & {{u}_{tt}}={{u}_{xx}},\text{ }x>0,\text{ }t>0 \\
& u(0,t)=0,\text{ }t>0 \\
& u(x,0)=x{{e}^{-{{x}^{2}}}},\text{ }0<x<\infty \\
& {{u}_{t}}(x,0)=0.
\end{aligned}
$

The condition $u(0,t)$ is new to me, since I usually apply the method when only having $u(x,0)$ and $u_t(x,0),$ what to do in this case?
 
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  • #2
The boundary and intial value conditions match at (0, 0) so I would just ignore it, then check to make sure my result satisfied that.
 
  • #3
Okay, I'll apply it then and see how it works, thanks!
 

FAQ: D'Lembert Method for Solving the Wave Equation with Boundary Conditions

What is the D'Lembert method application?

The D'Lembert method application is a mathematical technique used in statistics to estimate the mean of a population based on a sample. It is also known as the Laplace-Gauss method.

How does the D'Lembert method application work?

The D'Lembert method application works by taking the sum of the squared differences between each data point in a sample and the sample mean, and dividing it by the sample size minus one. This value is then used to calculate the estimated mean of the population.

When should the D'Lembert method application be used?

The D'Lembert method application is best used when the sample size is small (less than 30) and the population is normally distributed. It is also useful when the population standard deviation is unknown.

What are the limitations of the D'Lembert method application?

The D'Lembert method application assumes that the population is normally distributed, which may not always be the case. It also does not work well with skewed data, and can give inaccurate results if the sample size is too small.

How is the D'Lembert method application different from other statistical methods?

The D'Lembert method application is a specific type of estimation method that is used to estimate the mean of a population. It differs from other statistical methods, such as hypothesis testing or regression analysis, which are used to test relationships between variables or make predictions.

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