Table of Contents
What is the difference between exact solution and numerical solution?
An exact solution is a symbolic representation of a value which solves a given equation exactly, while a numerical solution is numerical (often decimal) representation of a value which solves a given equation exactly or approximately.
What are numerical solutions?
A numerical solution is an approximation to the solution of a mathematical equation, often used where analytical solutions are hard or impossible to find. All numerical solutions are approximations, some better than others, depending on the context of the problem and the numerical method used.
What is a numerical solution of a differential equation?
In a differential equation the unknown is a function, and the differential equation relates the function itself to its derivative(s). We then con- sider how first order equations can be solved numerically by the simplest method, namely Euler’s method.
What is numerical solution for civil engineering?
Numerical methods in Civil Engineering are now used routinely in structural analysis to determine the member forces and moments in structural systems, prior to design.
What is an exact function in math?
A first-order differential equation (of one variable) is called exact, or an exact differential, if it is the result of a simple differentiation. The function defined implicitly by x2y + x + y2 = c will solve the original equation.
Why is exact solution important?
It is significant that many equations of physics, chemistry, and biology contain empirical parameters or empirical functions. Exact solutions allow researchers to design and run experiments, by creating appropriate natural (initial and boundary) conditions, to determine these parameters or functions.
What is the importance of numerical methods?
The numerical methods are used for deeper understanding to predict the anomalies which are not possible in the analytical methods because the analytical method can solve only two or three unknown variables but numerical methods can do much more than it very accurately.
What is the difference between analytical and empirical?
empirical: based on, concerned with, or verified by observation or experience. analytical: based on analysis or logic.