7-A Solved problem 9-5 LU decomposition.
Solved problem 9-5 LU decomposition from reference book Numerical methods for engineers. We will verify our solution with the author’s solution.
Numerical analysis
The numerical analysis falls into several subdivisions, as follows
1-Introduction to numerical analysis.
2-Solving non-linear equations.
3-Solving Linear equations.
4-Interpolation.
6- Solved problem for x-y-z values by LU decomposition.
The solved problem for x-y-z values by using the LU decomposition. for three simultaneous equations. Step by step illustration is explained.
5A- Second solved problem-LU decomposition-3×3 matrix.
The second solved problem-LU decomposition for the 3×3 matrices, how to get x,y,z values for three simultaneous equations?
5- First solved problem-LU decomposition for the 3×3 matrix
This post illustrates the first solved problem-LU decomposition for the 3×3 matrix. Step by step guide to solve 3 simultaneous equations by the LU method?
4-Derive the expression for L-U values for-3×3 matrix.
Step-by-step guide on how to derive the expression for L-U values for-3×3 matrix using Doolittle’s method?
3-How to solve for x-y by L-U Decomposition?
How to solve for x-y by L-U Decomposition? Illustration by Gauss elimination for L and U matrices.
2- Easy illustration for LU decomposition for 2×2 matrix.
How to use the Lu decomposition method for a 2×2 matrix? A step-by-step guide to find L and U values?
1- Easy introduction to the Inverse of a Matrix-2×2 matrix.
How to get the inverse of a matrix by creating an identity matrix. A solved example is given for the inverse of a 2×2 matrix.
9-Maximum deflection distance by Newton-Raphson method.
Maximum deflection distance for a simply supported beam under triangular load numerically. How to use the Newton-Raphson method for root findings?
8- Structural analysis numerically by Newton-Raphson method.
Perform structural analysis using the Newton-Raphson method for a beam under uniformly distributed load and get the maximum deflection point location.
7A-Solved problem-8 by Modified Newton-Raphson method
A solved problem-8 by modified newton Raphson Method. A step-by-step guide comparison is made between the newton method and the modified Newton Raphson method.
7- An Easy Guide to Modified Newton-Raphson method.
The Modified Newton-Raphson method is another method for root finding. A simple modification to the previous method of Newton -Raphson was introduced.
6a- Two Solved problems for Newton-Raphson method.
Two solved problems for Newton-Raphson method for root extraction or roots finding are presented in this post.
6- Newton-Raphson method-Easy approach
Newton-Raphson method. is another method for roots finding. The derivation of this method is based on the linear approximation method.
5A-Practice problems with linear approximation
In this post, there are practice problems with linear approximation. these pr practice problems are using step-by-step illustration.