Epalli (American Journal of Innovation in Science and Engineering (AJISE)), 2025
Much research has been done regarding the Newton Coates method and generally the results that are... more Much research has been done regarding the Newton Coates method and generally the results that are available are about the trapezoidal method and the Sampson method and not much attention is paid to the higher levels of the Newton Coates method. This article has been written to find out what is the relationship between the high-order Newton-Cotes method and study behavior of error in high order methods. In this research numerical integration preformed, Newton Coates method is examined in detail and formulate the two points, three points, four points up to eight points are will investigate. Furthermore, this study showed that, analyze the errors of each method and show the relation between two consecutive Newton Coates methods. On the other hand, the research showed that, odd point's method would be better. It is worth mentioning that to obtain these methods, and in this study the researcher used the Lagrange interpolator polynomial.
International journal of advanced research, May 31, 2019
Since mathematics is a science of communication between us and the scientific sciences, in partic... more Since mathematics is a science of communication between us and the scientific sciences, in particular it introduces all the rules and problems as formulas, and searches for a solution. A part of the mathematics that is widely used in all sciences is the differential equation that will be studied in this dissertation. Each parts of these equations has its own method for solving, and we have generally studied the analytic methods in the calculus, and here we will introduce the numerical solutions. It is worth noting that in analytic methods cannot gives solution, for all equations this is where scientists have discovered the numerical methods that can be solved by those methods for those equations that are not solved in an analytical methods. In this Article, we first introduce differential equations and introduce a number of elementary topics for introduction so that the reader will get acquainted with these definitions and issues before the start of the process. Later in this article, one basic methods will be studied, the single step method, respectively, which relate to the initial value problem. Here we will examine in detail and analyze all the ways in which these methods are available. In the next step, all the good nesses, advantages, disadvantages that exist between these methods will be discussed, and also a comparative study we will have in this paper.
Since mathematics is a science of communication between us and the scientific sciences, in partic... more Since mathematics is a science of communication between us and the scientific sciences, in particular it introduces all the rules and problems as formulas, and searches for a solution. A part of the mathematics that is widely used in all sciences is the differential equation that will be studied in this dissertation. Each parts of these equations has its own method for solving, and we have generally studied the analytic methods in the calculus, and here we will introduce the numerical solutions. It is worth noting that in analytic methods cannot gives solution, for all equations this is where scientists have discovered the numerical methods that can be solved by those methods for those equations that are not solved in an analytical methods. In this Article, we first introduce differential equations and introduce a number of elementary topics for introduction so that the reader will get acquainted with these definitions and issues before the start of the process. Later in this article, one basic methods will be studied, the single step method, respectively, which relate to the initial value problem. Here we will examine in detail and analyze all the ways in which these methods are available. In the next step, all the good nesses, advantages, disadvantages that exist between these methods will be discussed, and also a comparative study we will have in this paper.
Epalli (American Journal of Innovation in Science and Engineering (AJISE)), 2025
Much research has been done regarding the Newton Coates method and generally the results that are... more Much research has been done regarding the Newton Coates method and generally the results that are available are about the trapezoidal method and the Sampson method and not much attention is paid to the higher levels of the Newton Coates method. This article has been written to find out what is the relationship between the high-order Newton-Cotes method and study behavior of error in high order methods. In this research numerical integration preformed, Newton Coates method is examined in detail and formulate the two points, three points, four points up to eight points are will investigate. Furthermore, this study showed that, analyze the errors of each method and show the relation between two consecutive Newton Coates methods. On the other hand, the research showed that, odd point's method would be better. It is worth mentioning that to obtain these methods, and in this study the researcher used the Lagrange interpolator polynomial.
International journal of advanced research, May 31, 2019
Since mathematics is a science of communication between us and the scientific sciences, in partic... more Since mathematics is a science of communication between us and the scientific sciences, in particular it introduces all the rules and problems as formulas, and searches for a solution. A part of the mathematics that is widely used in all sciences is the differential equation that will be studied in this dissertation. Each parts of these equations has its own method for solving, and we have generally studied the analytic methods in the calculus, and here we will introduce the numerical solutions. It is worth noting that in analytic methods cannot gives solution, for all equations this is where scientists have discovered the numerical methods that can be solved by those methods for those equations that are not solved in an analytical methods. In this Article, we first introduce differential equations and introduce a number of elementary topics for introduction so that the reader will get acquainted with these definitions and issues before the start of the process. Later in this article, one basic methods will be studied, the single step method, respectively, which relate to the initial value problem. Here we will examine in detail and analyze all the ways in which these methods are available. In the next step, all the good nesses, advantages, disadvantages that exist between these methods will be discussed, and also a comparative study we will have in this paper.
Since mathematics is a science of communication between us and the scientific sciences, in partic... more Since mathematics is a science of communication between us and the scientific sciences, in particular it introduces all the rules and problems as formulas, and searches for a solution. A part of the mathematics that is widely used in all sciences is the differential equation that will be studied in this dissertation. Each parts of these equations has its own method for solving, and we have generally studied the analytic methods in the calculus, and here we will introduce the numerical solutions. It is worth noting that in analytic methods cannot gives solution, for all equations this is where scientists have discovered the numerical methods that can be solved by those methods for those equations that are not solved in an analytical methods. In this Article, we first introduce differential equations and introduce a number of elementary topics for introduction so that the reader will get acquainted with these definitions and issues before the start of the process. Later in this article, one basic methods will be studied, the single step method, respectively, which relate to the initial value problem. Here we will examine in detail and analyze all the ways in which these methods are available. In the next step, all the good nesses, advantages, disadvantages that exist between these methods will be discussed, and also a comparative study we will have in this paper.
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Papers by Nikzad Jamali