StudentShare
Contact Us
Sign In / Sign Up for FREE
Search
Go to advanced search...

Comparing Eulers Method with Numerical Methods - Thesis Example

Cite this document
Summary
Comparing Euler’s Method with Numerical Methods Name Institution Comparing Euler’s Method with Numerical Methods Introduction Differential equations are equations that are used to describe systems that are undergoing change simultaneously. They are applied in numerous and different spheres of life including engineering, physics, social sciences, economics as well as biology…
Download full paper File format: .doc, available for editing
GRAB THE BEST PAPER97.7% of users find it useful
Comparing Eulers Method with Numerical Methods
Read Text Preview

Extract of sample "Comparing Eulers Method with Numerical Methods"

Download file to see previous pages

Nonetheless, differentiation of equation expressing these systems and shapes was noted to be quite complex. Moreover, these equations are only capable of describing extremely large systems and shapes, so pure mathematical analysis on them is quite impossible. The complex nature of these systems led to the usefulness of numerical approximation and computer simulations. Therefore, this paper will analyze Euler’s method in differentiating these complex mathematical equations. Notably, the numerical approximation techniques that are applied in solving the differential equation were thought of and developed long before the existence of the programmable computers.

During the Second World War, people (particularly women) used mechanical calculators (in their rooms) to solve differential equations for war purposes. However, the introduction and increase in programmable computers and computer applications have decreased the cost and increased the speed, thereby increasingly easing solving the difference equations of complex systems (Kuang and Cong, 2007). For example, laptops can easily compute a long term interjectory of over one million interacting molecules.

For about five to ten years ago, this problem seemed inaccessible to even the then fastest analog supercomputers. This essay will introduce the fundamental principle of numerical approximation and relate to geometry and curved surfaces. Thereafter, it will analyze how simple geometric problems can be handled using Euler’s method. Generally, numerical differential equations are always represented in the equation or functions, f. These functions can handle a wider range of ordinary differential equation (ODEs) and partial differential equations (PDEs).

A system of ordinary differential equations can contain any number of unknown functions. However, all these functions must be a derivative of a single independent variable, t that is the same for other functions (Kuang and Cong, 2007). On the other hand, partial differential equations often have two or more independent variables. Differential Equations There are numerous ways of solving differential equations. However, there are fundamental equations upon which all other equations are built. The first order system of differential equation takes the simplest order dy/dt = f(y, t) or y? = f(x, y).

Where dy/dy represents the change in y with time and f(y, t) is a function of variables y and t. notably, there are numerous notations for the change d/dt. The most common ones include ? and y’. This equation satisfies numerical integration that means computation from initial point y0 (the initial condition) to the other successive conditions y1, y2, y3 … since differential equations cannot be solved analytically, they take an algorithm that computes the function or equation as precise as possible, that is, yn+1 from yn.

In some cases, y may be a vector while the evolution equation may be non-linear differential equations. Problem Formulation The main theme of this essay is to use first order differential to solve differential equation under certain set conditions. Consider that the fundamental differential equation of the first order of ordinary differential equation is dy/dx = f(x, y) with the initial boundary condition being y(x0) = y0. Approximate the function y(x) over the sample values of xn

...Download file to see next pages Read More
Cite this document
  • APA
  • MLA
  • CHICAGO
(“Comparing Eulers Method with Numerical Methods Thesis”, n.d.)
Comparing Eulers Method with Numerical Methods Thesis. Retrieved from https://studentshare.org/mathematics/1400717-comparing-eulers-method-with-numerical-methods
(Comparing Eulers Method With Numerical Methods Thesis)
Comparing Eulers Method With Numerical Methods Thesis. https://studentshare.org/mathematics/1400717-comparing-eulers-method-with-numerical-methods.
“Comparing Eulers Method With Numerical Methods Thesis”, n.d. https://studentshare.org/mathematics/1400717-comparing-eulers-method-with-numerical-methods.
  • Cited: 0 times

CHECK THESE SAMPLES OF Comparing Eulers Method with Numerical Methods

Computional Fluid Dynamics for Filters

The reason for the importance of CFD becomes more evident as numerical equations governing the relationship between the three properties, density, viscosity and compression in space and time have to be solved to greater detail.... This paper ''Computional Fluid Dynamics for Filters'' tells that Dynamics is the study of the motion of objects and Fluid Dynamics is the study of the motion of fluids....
27 Pages (6750 words) Essay

Aerodynamic Shape Optimization

The CFD based design approaches are normally classified into three different methods namely – inverse surface models, inverse field model and numerical optimization models.... When the design variables goes over 1,00,000 the conventional methods would soon approach its limits.... The numerical models have been widely accepted in the design process and have clearly established their advantages over the conventional design process.... Thus the final objective of the aerodynamic design is, to arrive at the best aerodynamic configuration that gives the best operational performance given the constrains, irrespective of the method chosen to achieve this....
6 Pages (1500 words) Dissertation

Jornal Article on Women's drug Users

The current study also found out that existing literatures concerning the topic commonly used quantitative research methods wherein the researchers conducted interviews and surveys with convicted, female drug consumers and dealers.... To address the topic efficiently, Bucur's research design includes both qualitative and quantitative research methods.... In the quantitative methods, Bucur conducts surveys and interviews with female inmates in selected penitentiaries in urban areas....
4 Pages (1000 words) Essay

Engineering Analysis

a Able to solve higher order differential equations- with this method, you can solve equations of more than second degree equations as compared with classical methods which allow us to solve only first and second degree order equations. d When dealing with Laplace Transform,… external force is either off or on for some irregular or regular period of time or the external force can either be an impulse (example is that the force lasts for a short time) a These methods yield erroneous results especially if they are used or applied mechanically without Its highly encouraged to use different methods apart from the above mentioned since they are able to yield precisely better results, a way to counter this problem....
6 Pages (1500 words) Assignment

Business Research Methods

nbsp; For example, in instances where the researcher has conducted a survey study through close-ended questionnaires, standard deviations and frequency distribution emerge as an ideal method for the translation of the data in question into numerical form and their subsequent summarization in graphical form.... nbsp; The said tool, which is highly cost-effect and uncomplicated, effectively allows for the numerical/graphical summarization of large volumes of primary data....
4 Pages (1000 words) Essay

Research Methods for Business

The paper “Research methods for Business” looks at two main types of research methods that can be adopted by researchers, i.... Qualitative or phenomenological methods allow the researcher to produce rich intensive data and this is normally achieved with from small numbers of people and moreover, they tend to provide more contextual data – which adds value to other data – while acknowledges the fundamental complexity of certain social phenomena (Walker, 1985)....
14 Pages (3500 words) Dissertation

The Nature and Philosophy of Social Science Method

Learning which questions to ask and which tools to use is essentially the business of research methods.... The central issue thus is the research methods of inquiry that science uses i.... Research methods have been categorized into either qualitative or quantitative.... In social sciences, there is much debate on the supremacy of quantitative methods (based on positivism) or qualitative inquiry that is based on interpretivism (Spratt, Walker and Robinson 2004, 7)....
10 Pages (2500 words) Research Paper

Research Methods for Business Students

A writer of the paper "Research methods for Business Students" outlines that objective of this market research would also be to understand people's perception towards the suburb and ways in which suburb has changed energy consumption pattern of respective residents.... Reason 2- buying and living in Lochiel Park by residents is a longitudinal process, which is why there is hardly any scope of employing short time interval driven observation method of data collection (Maxwell, 2005)....
6 Pages (1500 words) Assignment
sponsored ads
We use cookies to create the best experience for you. Keep on browsing if you are OK with that, or find out how to manage cookies.
Contact Us