Numerical analysis - "Engineering Oasis"

3-How to solve for x-y by L-U Decomposition?

September 17, 2025November 20, 2020 by Maged kamel

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.

September 17, 2025November 14, 2020 by Maged kamel

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.

September 22, 2025October 15, 2020 by Maged kamel

Easy introduction to Inverse of a Matrix-2x2 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.

July 23, 2024September 30, 2020 by Maged kamel

brief illustration for -Post 9-maximium deflection distance

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.

March 21, 2024September 20, 2020 by Maged kamel

brief illustration for -Post 8-structural analysis byNewton-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

January 11, 2024September 19, 2020 by Maged kamel

brief illustration for -Post 7A-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.

March 21, 2024September 10, 2020 by Maged kamel

brief illustration -Post 7-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.

June 15, 2025September 8, 2020 by Maged kamel

brief illustration for-Post 6A-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

March 21, 2024September 7, 2020 by Maged kamel

brief illustration for -Post 6-Newton-Raphson method

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

December 19, 2024August 14, 2020 by Maged kamel

In this post, there are practice problems with linear approximation. these pr practice problems are using step-by-step illustration.

5- What is the Linear Approximation method?

March 21, 2024August 5, 2020 by Maged kamel

brief illustration for -Post 5-Linear approximation method

Introduction to linear approximation, what is a linear approximation equation?

4-Fixed-point iteration and how to use it?

March 21, 2024July 13, 2020 by Maged kamel

brief illustration for -Post 4-Fixed point iteration method

In numerical analysis, fixed-point iteration is a method of computing the roots of a function by changing the typical f(x)=y form to another form which is x= g(x).

3- Quick start to False position method for roots finding.

March 21, 2024June 15, 2020 by Maged kamel

brief illustration for -Post 3-False position method

The false position method is another numerical method for roots finding, The same Solved problem will be used to get the root for f(x) by false position.

2- Easy introduction to Bisection method for roots findings.

March 4, 2025August 20, 2019 by Maged kamel

Brief illustration for -Post 2-bisection method

The bisection method can be done by taking the average value of the horizontal distance between points of brackets, and then substitute it in the function.

1a-What is synthetic division? Numerical Analysis-part 2

March 3, 2025July 5, 2019 by Maged kamel

brief introduction for Post 1A-Numerical analysis -part 2

Numerical analysis-part 2-What is synthetic division? Solved problems for synthetic divisions are included.