Heat and mass transfer in greenhouse, Heat Flux in a Grain Bin, Suspension systems in tractors, Fluid Flow in a Pipe, Concentration in a Chemical Reactor, Falling Water Table, etc.
Answered by Ramin Shamshiri, U. of Florida at Gainesville.
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.
A differential equation is a measure of change. If differencing with respect to time, it is the rate of change. Location, when differentiated, gives velocity. Velocity, when differentiated, gives acceleration. There are significant applications across all aspects of science.
ordinary differential equation is obtained only one independent variable and partial differential equation is obtained more than one variable.
It is the solution of a differential equation without there being any restrictions on the variables (No boundary conditions are given). Presence of arbitrary constants indicates a general solution, the number of arbitrary constants depending on the order of the differential equation.
Yes, it is.
There is no application of differential equation in computer science
Many real world problems can be represented by first order differential equation. Some applications of differential equation are radio-active decay and carbon dating, population growth and decay, warming/cooling law and draining a tank.
Poisson's equation is a partial differential equation of elliptic type. it is used in electrostatics, mechanical engineering and theoretical physics.
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.
Many real world problems can be represented by first order differential equation. Some applications of differential equation are radio-active decay and carbon dating, population growth and decay, warming/cooling law and draining a tank.
A differential equation have a solution. It is continuous in the given region, but the solution of the impulsive differential equations have piecewise continuous. The impulsive differential system have first order discontinuity. This type of problems have more applications in day today life. Impulses are arise more natural in evolution system.
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.
Differential equation is defined in the domain except at few points (may be consider the time domain ti ) may be (finite or countable) in the domain and a function or difference equation is defined at each ti in the domain. So, differential equation with the impulsive effects we call it as impulsive differential equation (IDE). The solutions of the differential equation is continuous in the domain. But the solutions of the IDE are piecewise continuous in the domain. This is due to the nature of impulsive system. Generally IDE have first order discontinuity. There are so many applications for IDE in practical life.
Differential equation is defined in the domain except at few points (may be consider the time domain ti ) may be (finite or countable) in the domain and a function or difference equation is defined at each ti in the domain. So, differential equation with the impulsive effects we call it as impulsive differential equation (IDE). The solutions of the differential equation is continuous in the domain. But the solutions of the IDE are piecewise continuous in the domain. This is due to the nature of impulsive system. Generally IDE have first order discontinuity. There are so many applications for IDE in practical life.
Applications of ordinary differential equations are commonly used in the engineering field. The equation is used to find the relationship between the various parts of a bridge, as seen in the Euler-Bernoulli Beam Theory.
A differential equation is a measure of change. If differencing with respect to time, it is the rate of change. Location, when differentiated, gives velocity. Velocity, when differentiated, gives acceleration. There are significant applications across all aspects of science.
ordinary differential equation is obtained only one independent variable and partial differential equation is obtained more than one variable.