# Runge-Kutta Methods – Algorithm, Implementation in C With Solved Examples

Runge-Kutta Method

Finding the solution of differential equation the Runge Kutta method give more accurate result. The Euler method is less efficient in practical problems

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# Category: Numerical Methods & Algorithms

# Runge-Kutta Methods – Algorithm, Implementation in C With Solved Examples

# Euler Method – Algorithm, Implementation in C With Solved Examples

# Simpson’s 1/3rd Rule – Algorithm, Implementation in C With Solved Examples

# Trapezoidal Rule – Algorithm, Implementation in C With Solved Examples

# LU Decomposition Method – Algorithm, Implementation in C With Solved Examples

# Gauss Seidel Method – Algorithm, Implementation in C With Solved Examples

# Gauss-Jacobi’s Iteration Method – Algorithm, Implementation in C With Solved Examples

# Newton-Raphson Method – Algorithm, Implementation in C With Solved Examples

# Iteration Method or Fixed Point Iteration – Algorithm, Implementation in C With Solved Examples

# Bisection Method – Algorithm, Implementation in C with Solved Examples

Runge-Kutta Method

Finding the solution of differential equation the Runge Kutta method give more accurate result. The Euler method is less efficient in practical problems

Euler Method for Differential Equation

Euler method is the most simple but crude method to solve differential equation of the form

\[\frac{dy}{dx}=f\left( x,y \right),~~~y\left( {{x}_{0}}

Simpson’s 1/3 rule

In Simpson’s 1/3 rule the interval [a, b] is divided into two equal sub-intervals by the points x0, x1, x2, where h

At first we deduce the general integration formula based on Newton’s forward interpolation formula and after that we will use it to formulate Trapezoidal Rule

LU Decomposition Method

LU Decomposition Method is also known as factorization or Crout’s reduction method. Let the system of linear equations be

\[Ax=b……….(1)\]

Where A,

Gauss Seidel Iteration Method

A simple modification of Jocobi’s iteration sometimes gives faster convergence, the modified method is known as Gauss Seidel method.

Let us

To find the solution of system of linear equations, in this article we will discuss Gauss-Jacobi’s iteration method.

Solution of System of Linear Equations

Generally,

To solve non-linear function of the real variable x we have already learned Bisection method and Iteration method, in this article we are going to

Iteration Method or Fixed Point Iteration

The iteration method or the method of successive approximation is one of the most important methods in numerical mathematics.

Bisection Method

The Bisection method is the most simplest iterative method and also known as half-interval or Bolzano method.

This method is based on the