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What is a drawback of trying to solve a partial differential equation explicitly?
As far as I'm aware a PDE can't be solved explicitly because of the nature of the equation. However, you can separate the variables of a PDE essentially turning it into multiple ODEs which then can be solved explicitly.
The draw back of this is that most terms in a PDE are a combination of variables, such as 3xy+2yz+xyz, rather than being separated neatly already (making separation into ODEs easy), such as x+y+z. In cases where the variables are jumbled up with each other, there are often faster and easier ways of solving the PDE than trying to separate the variables into ODEs and solving explicitly.
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What is the difference between an ordinary differential equation and a partial differential equation?
ordinary differential equation is obtained only one independent variable and partial differential equation is obtained more than one variable.
Heat equation partial differential?
Yes, it is.
What is a numerical solution of a partial differential equation?
Some partial differential equations do not have analytical solutions. These can only be solved numerically.
What are the applications of partial differential equations in computer science?
All the optimization problems in Computer Science have a predecessor analogue in continuous domain and they are generally expressed in the form of either functional differential equation or partial differential equation. A classic example is the Hamiltonian Jacobi Bellman equation which is the precursor of Bellman Ford algorithm in CS.
What is nonlinear ordinary differential equation?
An ordinary differential equation is an equation relating the derivatives of a function to the function and the variable being differentiated against. For example, dy/dx=y+x would be an ordinary differential equation. This is as opposed to a partial differential equation which relates the partial derivatives of a function to the partial variables such as d²u/dx²=-d²u/dt². In a linear ordinary differential equation, the various derivatives never get multiplied together, but they can get multiplied by the variable. For example, d²y/dx²+x*dy/dx=x would be a linear ordinary differential equation. A nonlinear ordinary differential equation does not have this restriction and lets you chain as many derivatives together as you want. For example, d²y/dx² * dy/dx * y = x would be a perfectly valid example
What is the difference between an ordinary differential equation and a partial differential equation?
ordinary differential equation is obtained only one independent variable and partial differential equation is obtained more than one variable.
Heat equation partial differential?
Yes, it is.
What is a numerical solution of a partial differential equation?
Some partial differential equations do not have analytical solutions. These can only be solved numerically.
Example of total partial and original differential equation?
An ordinary differential equation (ODE) has only derivatives of one variable.
What does PDE stand for?
PDE stands for Partial Differential Equation
What is monge's Method?
Monge's method, also known as the method of characteristics, is a mathematical technique used to solve certain types of partial differential equations. It involves transforming a partial differential equation into a system of ordinary differential equations by introducing characteristic curves. By solving these ordinary differential equations, one can find a solution to the original partial differential equation.
What are the applications of partial differential equations in computer?
All the optimization problems in Computer Science have a predecessor analogue in continuous domain and they are generally expressed in the form of either functional differential equation or partial differential equation. A classic example is the Hamiltonian Jacobi Bellman equation which is the precursor of Bellman Ford algorithm in CS.
What are the applications of partial differential equations in computer science?
All the optimization problems in Computer Science have a predecessor analogue in continuous domain and they are generally expressed in the form of either functional differential equation or partial differential equation. A classic example is the Hamiltonian Jacobi Bellman equation which is the precursor of Bellman Ford algorithm in CS.
What is nonlinear ordinary differential equation?
An ordinary differential equation is an equation relating the derivatives of a function to the function and the variable being differentiated against. For example, dy/dx=y+x would be an ordinary differential equation. This is as opposed to a partial differential equation which relates the partial derivatives of a function to the partial variables such as d²u/dx²=-d²u/dt². In a linear ordinary differential equation, the various derivatives never get multiplied together, but they can get multiplied by the variable. For example, d²y/dx²+x*dy/dx=x would be a linear ordinary differential equation. A nonlinear ordinary differential equation does not have this restriction and lets you chain as many derivatives together as you want. For example, d²y/dx² * dy/dx * y = x would be a perfectly valid example
In mathematics what does the abbreviation PDE stand for?
The abbreviation PDE stands for partial differential equation. This is different from an ordinary differential equation in that it contains multivariable functions rather than single variables.
Are there any applications of poisson's equation?
Poisson's equation is a partial differential equation of elliptic type. it is used in electrostatics, mechanical engineering and theoretical physics.
Where you use Partial Differential Equation in your daily life?
It's all around you, starting with equation of diffusion and ending with equation of propagation of sound and EM waves.
