The quantity z is called a functional of f(x) in the interval [a,b] if it depends on all the values of f(x) in [a,b]..sir, I read this online
“”if z=2 is the output of f(x) and the interval is ( 1, 3) can I say z=2 is a functional of f(x)””

The question does not appear sensible even with an ordinary function. To illustrate, let me cast it this way: If y=f(x), and y=10 at a point, can you say y=10 is a function of x?

A Mathematica solution to the problem example in Reddy 29-30 is provided for you at http://1drv.ms/1DpApnC . Download this solution and do the following: 1. Classify the Solution methods used. 2. Formulate solutions for Collocation, Least Squares and the Garlekin Method. Use at least three or four trial functions or collocation points.

I was going through some solved examples using Galerkin method and Variational method.. the question to the Galerkin method has boundary conditions of the form 1«x«2, y(1)=y(2)=0. while the question to the Variational method was given x=0 y’=dy/dx=0 and x=1 y=y2….. I understood both solutions, but my question is that in choosing a method to solve a problem, do we have to base our decision on the type of conditions both problems present?

I want to believe both questions should be solvable using one same method? But with the procedures I learnt from these examples, the different forms of boundary conditions makes both problems appear solvable with their distinct methods like the examples did.

i need to access your lecture notes on finite element analysis.

The uploaded notes have been updated as at 20:15 April 15, 2015

The quantity z is called a functional of f(x) in the interval [a,b] if it depends on all the values of f(x) in [a,b]..sir, I read this online

“”if z=2 is the output of f(x) and the interval is ( 1, 3) can I say z=2 is a functional of f(x)””

The question does not appear sensible even with an ordinary function. To illustrate, let me cast it this way: If y=f(x), and y=10 at a point, can you say y=10 is a function of x?

A Mathematica solution to the problem example in Reddy 29-30 is provided for you at http://1drv.ms/1DpApnC . Download this solution and do the following: 1. Classify the Solution methods used. 2. Formulate solutions for Collocation, Least Squares and the Garlekin Method. Use at least three or four trial functions or collocation points.

Good day sir!

I was going through some solved examples using Galerkin method and Variational method.. the question to the Galerkin method has boundary conditions of the form 1«x«2, y(1)=y(2)=0. while the question to the Variational method was given x=0 y’=dy/dx=0 and x=1 y=y2….. I understood both solutions, but my question is that in choosing a method to solve a problem, do we have to base our decision on the type of conditions both problems present?

I want to believe both questions should be solvable using one same method? But with the procedures I learnt from these examples, the different forms of boundary conditions makes both problems appear solvable with their distinct methods like the examples did.