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The following partial differential equation is defined for u:u (x, y)
The set auxiliary conditions necessary to solve the equation uniquely, is
The set auxiliary conditions necessary to solve the equation uniquely, is
- a)three initial conditions
- b)three boundary conditions
- c)two initial conditions and one boundary condition
- d)one initial conditions and two boundary conditions
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The following partial differential equation is defined for u:u (x, y)T...
Given:
This is a 1-D Heat equation. It measures temperature distribution in a uniform rod.
The general solution is u = f(x, t)
Auxiliary solutions include both initial and boundary conditions.
1) Number of initial conditions = Highest order of time derivative in partial differential = 1
2) The number of boundary conditions:
To solve this partial differential equation, it needs to be integrated twice that will introduce two arbitrary constants.
Hence 2 boundary conditions and 1 initial condition are required to solve this Partial differential equation.
This is a 1-D Heat equation. It measures temperature distribution in a uniform rod.
The general solution is u = f(x, t)
Auxiliary solutions include both initial and boundary conditions.
1) Number of initial conditions = Highest order of time derivative in partial differential = 1
2) The number of boundary conditions:
To solve this partial differential equation, it needs to be integrated twice that will introduce two arbitrary constants.Hence 2 boundary conditions and 1 initial condition are required to solve this Partial differential equation.
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The following partial differential equation is defined for u:u (x, y)The set auxiliary conditions necessary to solve the equation uniquely, isa)three initial conditionsb)three boundary conditionsc)two initial conditions and one boundary conditiond)one initial conditions and two boundary conditionsCorrect answer is option 'D'. Can you explain this answer?
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