Question

用matlab解微分方程

Answer 1

楼主是要解析解吧

dsolve('Dy=A/V-B/V*sqrt(2*g*y)','y(0)=h0','t')

ans =

(2^(1/2)*A + 2^(1/2)*A*lambertw(0, (2^(1/2)*B*g^(1/2)*exp(-(A + B^2*g*(t/V - (A*(log(-(exp(-(A + 2^(1/2)*B*(g*h0)^(1/2))/A)*(2*B*(g*h0)^(1/2) + 2^(1/2)*A))/(2*B*g^(1/2))) + 1))/(B^2*g)))/A))/A))^2/(4*B^2*g)
(2^(1/2)*A + 2^(1/2)*A*lambertw(0, (2^(1/2)*B*g^(1/2)*exp(-(A + B^2*g*(t/V - (A*(log((exp(-(A - 2^(1/2)*B*(g*h0)^(1/2))/A)*(2*B*(g*h0)^(1/2) - 2^(1/2)*A))/(2*B*g^(1/2))) + 1))/(B^2*g)))/A))/A))^2/(4*B^2*g)

lambert w叫Ω函数或乘数对数，属于复变函数的范畴

所以还是用数值解的好

Answer 2

1. 编写微分方程的函数保存为tmp_diff.m

function dh = tmp_diff(t,h,A,B,g,V)
dh = V/A-B/A*(2*g*h)^0.5;
return

2. 主程序中给定A，B，V，g, h0的值，再给定tspan，即时间范围
example:
A = 1; B =2; g =10; V = 1; h0=0;tspan = 0:1:2;
[t h] = ode15s(@tmp_diff,tspan,h0,[ ],A,B,g,V);

也可以是用ode45来计算
[t h] = ode45(@tmp_diff,tspan,h0,[ ],A,B,g,V);
>> [t h]

ans =

0 0
1.0000 0.0125
2.0000 0.0125

追问

我是想在结果中用A、B、V、g h0表示

追答

matlab是数字运算，不能带字符串运算的吧