How do I proceed from here solving partial differential equation with boundary conditions
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I am solving a differential problem with boundary conditions and stuck at a point and looking for helps.Here is what I did.
The problem is: Solve the differential equation
$$frac{partial u}{partial t} = frac{partial^2u}{partial x^2} + u$$
with boundary conditions$$ u(0,t)=u(1,t)=0$$
I tried using separating variable method where $$ u(x,t)=X(x)T(t)$$ and got $$XT'=X''T+1$$ and lost how to proceed.
How do I proceed to solve this?
pde
edited Nov 18 at 10:06
Jean Marie
28.2k41848
asked Nov 18 at 9:51
Ryanian
1
add a comment |
up vote
0
down vote
favorite
I am solving a differential problem with boundary conditions and stuck at a point and looking for helps.Here is what I did.
The problem is: Solve the differential equation
$$frac{partial u}{partial t} = frac{partial^2u}{partial x^2} + u$$
with boundary conditions$$ u(0,t)=u(1,t)=0$$
I tried using separating variable method where $$ u(x,t)=X(x)T(t)$$ and got $$XT'=X''T+1$$ and lost how to proceed.
How do I proceed to solve this?
pde
edited Nov 18 at 10:06
Jean Marie
28.2k41848
asked Nov 18 at 9:51
Ryanian
1
A notational remark : It is a partial differential equation (PDE) as opposed to an ordinary differential equation (ODE). So the convention is to use $partial$ instead of the usual $d$. I have done it on your text.
– Jean Marie
Nov 18 at 9:58
It is a variant of "heat Partial Differential equation" : see equation (4) in {tutorial.math.lamar.edu/Classes/DE/TheHeatEquation.aspx} and what follows.
– Jean Marie
Nov 18 at 10:05
1
its $XT'=X''T+XT$ then separate
– Isham
Nov 18 at 10:12
How do I solve it if there is no initial condition given?
– Ryanian
Nov 18 at 19:53
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I am solving a differential problem with boundary conditions and stuck at a point and looking for helps.Here is what I did.
The problem is: Solve the differential equation
$$frac{partial u}{partial t} = frac{partial^2u}{partial x^2} + u$$
with boundary conditions$$ u(0,t)=u(1,t)=0$$
I tried using separating variable method where $$ u(x,t)=X(x)T(t)$$ and got $$XT'=X''T+1$$ and lost how to proceed.
How do I proceed to solve this?
pde
edited Nov 18 at 10:06
Jean Marie
28.2k41848
asked Nov 18 at 9:51
Ryanian
1
I am solving a differential problem with boundary conditions and stuck at a point and looking for helps.Here is what I did.
The problem is: Solve the differential equation
$$frac{partial u}{partial t} = frac{partial^2u}{partial x^2} + u$$
with boundary conditions$$ u(0,t)=u(1,t)=0$$
I tried using separating variable method where $$ u(x,t)=X(x)T(t)$$ and got $$XT'=X''T+1$$ and lost how to proceed.
How do I proceed to solve this?
pde
pde
edited Nov 18 at 10:06
Jean Marie
28.2k41848
asked Nov 18 at 9:51
Ryanian
1
edited Nov 18 at 10:06
Jean Marie
28.2k41848
asked Nov 18 at 9:51
Ryanian
1
edited Nov 18 at 10:06
Jean Marie
28.2k41848
edited Nov 18 at 10:06
Jean Marie
28.2k41848
edited Nov 18 at 10:06
Jean Marie
28.2k41848
28.2k41848
asked Nov 18 at 9:51
Ryanian
1
asked Nov 18 at 9:51
Ryanian
1
asked Nov 18 at 9:51
Ryanian
1
1
A notational remark : It is a partial differential equation (PDE) as opposed to an ordinary differential equation (ODE). So the convention is to use $partial$ instead of the usual $d$. I have done it on your text.
– Jean Marie
Nov 18 at 9:58
It is a variant of "heat Partial Differential equation" : see equation (4) in {tutorial.math.lamar.edu/Classes/DE/TheHeatEquation.aspx} and what follows.
– Jean Marie
Nov 18 at 10:05
1
its $XT'=X''T+XT$ then separate
– Isham
Nov 18 at 10:12
How do I solve it if there is no initial condition given?
– Ryanian
Nov 18 at 19:53
add a comment |
A notational remark : It is a partial differential equation (PDE) as opposed to an ordinary differential equation (ODE). So the convention is to use $partial$ instead of the usual $d$. I have done it on your text.
– Jean Marie
Nov 18 at 9:58
It is a variant of "heat Partial Differential equation" : see equation (4) in {tutorial.math.lamar.edu/Classes/DE/TheHeatEquation.aspx} and what follows.
– Jean Marie
Nov 18 at 10:05
1
its $XT'=X''T+XT$ then separate
– Isham
Nov 18 at 10:12
How do I solve it if there is no initial condition given?
– Ryanian
Nov 18 at 19:53
A notational remark : It is a partial differential equation (PDE) as opposed to an ordinary differential equation (ODE). So the convention is to use $partial$ instead of the usual $d$. I have done it on your text.
– Jean Marie
Nov 18 at 9:58
A notational remark : It is a partial differential equation (PDE) as opposed to an ordinary differential equation (ODE). So the convention is to use $partial$ instead of the usual $d$. I have done it on your text.
– Jean Marie
Nov 18 at 9:58
It is a variant of "heat Partial Differential equation" : see equation (4) in {tutorial.math.lamar.edu/Classes/DE/TheHeatEquation.aspx} and what follows.
– Jean Marie
Nov 18 at 10:05
It is a variant of "heat Partial Differential equation" : see equation (4) in {tutorial.math.lamar.edu/Classes/DE/TheHeatEquation.aspx} and what follows.
– Jean Marie
Nov 18 at 10:05
1
1
its $XT'=X''T+XT$ then separate
– Isham
Nov 18 at 10:12
its $XT'=X''T+XT$ then separate
– Isham
Nov 18 at 10:12
How do I solve it if there is no initial condition given?
– Ryanian
Nov 18 at 19:53
How do I solve it if there is no initial condition given?
– Ryanian
Nov 18 at 19:53
add a comment |
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A notational remark : It is a partial differential equation (PDE) as opposed to an ordinary differential equation (ODE). So the convention is to use $partial$ instead of the usual $d$. I have done it on your text.
– Jean Marie
Nov 18 at 9:58
It is a variant of "heat Partial Differential equation" : see equation (4) in {tutorial.math.lamar.edu/Classes/DE/TheHeatEquation.aspx} and what follows.
– Jean Marie
Nov 18 at 10:05
1
its $XT'=X''T+XT$ then separate
– Isham
Nov 18 at 10:12
How do I solve it if there is no initial condition given?
– Ryanian
Nov 18 at 19:53