응용수학 편미분 방정식 좀 풀어주세요.

[위젯]

직장 다니다가 학교로 돌아가려고 수학 문제 좀 풀고 있는데,

너무 오래 전에 손을 놓아서, 잘 모르겠네요.

편미분방정식 잘 푸시는 분들 아래 문제 좀 풀어 주세요.ㅜㅜ

감사합니다.

1) Consider the partial differential equation:

Here ψ is a function of x and t. No boundary conditions are specified, in that the
differential equation remains valid for all x and t. The function δ(x) is the dirac delta
function. Note that exponentiation is used twice here. The second term on the right
hand side of the equation could also be written:

Here i is the imaginary constant. The value of the second term on the right hand side
at t=4 is thus:

Here only the first five digits have been shown of the decimal representation of the
resulting complex value.
Solve for ψ. If the differential equation is singular, any nontrivial solution is
acceptable.

2) Consider the partial differential equation:

Here h is a constant. We have h<<1. At x=0, we have:

Calculate ψ(x,t) for x>=0 to first order accuracy in h. It is acceptable if the solution
diverges for large x, but for finite x the solution is also finite.