The post NUMERICAL METHODS FOR SOLVING PARTIAL DIFFERENTIAL EQUATION first appeared on Chris Project Research.

]]>Numerical methods were first put into use as an effective tool for solving partial differential equations (PDEs) by John von Neumann in the mid-1940s.

In a 1949 letter von Neumann wrote “the entire computing machine is merely one component of a greater whole, namely, of the unity formed by the computing machine, the mathematical problems that go with it, and the type of planning which is called by both.

” The “greater whole” is viewed today as scientific computation: over the past sixty years, scientific computation has emerged as the most versatile tool to complement theory and experiments, and numerical methods for solving PDEs are at the heart of many of today’s advanced scientific computations.

Numerical solutions found their way from financial models on Wall Street to traffic models on Main Street. This study provide solution to partial differential equation using numerical methods.

**TABLE OF CONTENTS**

CHAPTER ONE: INTRODUCTION

1.1 Background of the Study

1.2 Statement of Research Problem

1.3 Aim and Objectives of Study

1.4 Scope of Study

1.5 Significance of Study

CHAPTER TWO: Literature Review

2.1 Examples of nonlinear PDEs

2.2. Examples of time-dependent PDEs. Atomic physics is dominated by the

2.3. Well-posed problems.

CHAPTER THREE

3.1 Numerical methods

3.1.1 Finite-difference methods.

3.1.2. Finite-element methods.

3.1.3. Finite-volume methods

3.1.4. Spectral methods.

CHAPTER FOUR

4.0 Basic Concepts in the Analysis of Numerical Methods

4.1. Consistency and order of accuracy.

4.2. Convergence and convergence rate

4.3. Stability of numerical methods.

4.4. From the linear to the nonlinear setup.

4.5. Challenges in numerical methods for nonlinear problems.

CHAPTER FIVE: Conclusion

References

The post NUMERICAL METHODS FOR SOLVING PARTIAL DIFFERENTIAL EQUATION first appeared on Chris Project Research.

]]>The post TIME SERIES ANALYSIS ON THE ROAD ACCIDENT IN OYO STATE NIGERIA FROM 2001-2017 first appeared on Chris Project Research.

]]>This research investigated the trend of accident in Oyo State, Nigeria. The data is collected from Federal Road Safety Agencies Oyo State chapter, it covered a period of 17years (2001-2017), this gives a view into the rate of accident in the state

More so, the analysis was done with statistical time series using E-view software as the tool analysis. It shows that the data on accident in Oyo State is not stationary at the first level of Augumented Dickey Fuller unit root test, which include intercept, trend/intercept and none. But the data set is stationary at the first differencing, which also include the same test equations. However, the data set on accident in Oyo State follows Autoregressive model, this applies to all the variable involved, the models are; minor accident Y=0.317904_{t-1 }+ 0.263939_{t-2 }+0.045332_{t-3} -0.097220_{t-4}– -0.061867_{t-5} + 0.029531_{t-6}+0.456775_{t-7} 0.043657_{t-8 } serious accident Y=0.317904_{t-1 }+ 0.6585055_{t-2 }+0.510975_{t-3} -0.38094_{t-4}– -0.671996_{t-5} + 0.459391_{t-6}+0.394592_{t-7} 0.037800_{t-8,} fatal accident and Total accident is Y=0.317904_{t-1 }+ 0.658505_{t-2 }+0.510975_{t-3} -0.38094_{t-4}– -0.671996_{t-5} + 0.459391_{t-6}+0.394592_{t-7} 0.037800_{t-8 }

Since the variable involve are not stationary, it shows clearly that the whole data set on accident is not constant in the variance, mean and autocorrelation. The coefficient of determination *R ^{2} *is 775%, this implies that 77.5% of the total accidents is explained by minor accident, serious accident and fatal accident.

Finally, alcohol used in driving is mostly common among commercial drivers, government should make laws and policy that will help these commercial drivers to prevent occasional recurrence of this situation, which is the major cause of road accident.

**TABLE OF CONTENTS**

CHAPTER ONE: INTRODUCTION

1.1 Background of the Study

1.2 Statement of the Problem

1.3 Aim and Objectives of the Study

1.4 Significance of the Study

1.5 Scope of the Study

1.6 Limitation of the Study

1.7 Organisation of the Study

CHAPTER TWO: LITERATURE REVIEW

2.1 Road Traffic Accidents

2.2 Review on Road Accidents in Nigeria

2.3 Causes of Road Traffic Accidents

CHAPTER THREE: METHODOLOGY

3.1 Time Series Data

3.2 Trend, Seasonality, Cycles and Residuals

3.3 Stationary Processes

3.4 Autoregressive-Moving-Average Model

3.5 Autoregressive Mode

3.6 Moving-Average Model

3.6.1 Note about the Error Terms

3.6.2 Specification In Terms of Lag Operator

3.6.3 Alternative Notation

3.7 Fitting Models

3.8 Arima Processes

3.9 Estimation of the Autocovariance Function

3.10 Identification of Arima Models

3.11 Parameter Estimation

3.12 Auto Regressive Integrated Moving Average (Arima).

3.13 Distributions of the Acf and Pacf

3.14 White Noise

3.15 The Turning Points Test

CHAPTER FOUR: DATA ANALYSIS AND PRESENTATION

4.1 Data Presentation

CHAPTER FIVE: SUMMARY, CONCLUSION AND RECOMMENDATION

5.1 Summary

5.2 Conclusion

5.3 Recommendations

References

The post TIME SERIES ANALYSIS ON THE ROAD ACCIDENT IN OYO STATE NIGERIA FROM 2001-2017 first appeared on Chris Project Research.

]]>The post SOLVING ORDINARY DIFFERENTIAL EQUATIONS USING POWER SERIES first appeared on Chris Project Research.

]]>In this work, we studied that power series method is the standard basic method for solving linear differential equations with variable coefficients. The solution usually take the form of power series; this explain the name power series method. We review some special second order ordinary differential equations. Power series method is described at ordinary point as well as at singular points (which can be removed called Frobenius method) of differential equations. The Frobenius method extends the simple series method to include negative and fractional powers and it also allows a natural extension involving logarithm terms. Few examples are presented on this method by solving special second order ordinary differential equations.

The post SOLVING ORDINARY DIFFERENTIAL EQUATIONS USING POWER SERIES first appeared on Chris Project Research.

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