## Which numerical method is best for ODE?

TZakrevskiy is right, RK4 or Runze-Kutta method is a robust technique for ODE. – L.K. Runge-Kutta methods are probably the most popular.

**Which method is Runge-Kutta method of 2nd order?**

k1 = f(tn,yn), k2 = f(tn + h,yn + hk1). This is the classical second-order Runge-Kutta method. It is also known as Heun’s method or the improved Euler method.

### What is Euler method in numerical analysis?

Euler’s method is based on approximating the graph of a solution y(x) with a sequence of tangent line approximations computed sequentially, in “steps”. Our first task, then, is to derive a useful formula for the tangent line approximation in each step.

**How many methods are there to solve ODE?**

two methods

There exist two methods to find the solution of the differential equation.

#### What is Picard’s method?

The Picard’s iterative method gives a sequence of approximations Y1(x), Y2(x), … Yk(x) to the solution of differential equations such that the nth approximation is obtained from one or more previous approximations.

**What is the difference between numerical analysis and numerical methods?**

A numerical method is an algorithm that takes numbers as input and produces numbers as output. Numerical analysis is a set of techniques you use to prove that a numerical method approximately solves a problem you’re interested in.

## What is the difference between numerical and analytical methods?

An analytical solution involves framing the problem in a well-understood form and calculating the exact solution. A numerical solution means making guesses at the solution and testing whether the problem is solved well enough to stop.

**How many integrations are involved in a second order system?**

For the case of a regular system of two second-order ODEs admitting three-dimensional Lie algebras, there are four functionally independent invariants. For example, consider the system of two second-order ODEs admitting the three-dimensional Lie algebra .

### What is the difference between Euler’s method and Euler’s modified method?

Generally the modified Euler method is more accurate than Euler method. In this work which concern with the accuracy of numerical solutions for first order differential equations. Euler and modified Euler methods have been applied in order to investigate the objective of the study.