项目描述
The program should implement the methods specified in the option. The implementation must not depend on a particular equation or system, or it must be localized. This means that implementations that allow the user to enter arbitrary (within the framework of permissible classes of problems) equations/systems of equations are preferred. All experiments should be performed for at least two or three different functions/systems, and for each function/system, the algorithms should be tested at different lengths. The result of the algorithm is that
It is one or more functions; for each function it is necessary (on the same graphical plane) to construct two graphs – obtained by experiment and “theoretical” – obtained from a pre-known analytical representation of this desired function. The method of conducting the experiment, therefore, consists in the fact that a certain equation or system is fixed, the solution of which is known in advance (obtained analytically by hand), and this solution is compared with the result of the work of numerical algorithms.
For an analytically defined function on a segment, make a series of grids of 100, 150, . . 600 knots. Each grid should be with equidistant or unequal nodes - depending on the specifics of the method specified in the option. If the task indicates two (or more) methods, or a family of methods (in particular, standard formulas (for example, the formulas of Newton, Stirling or Bessel) set a family of similar methods of different order), you need to perform a comparison of the effectiveness of the method.
These methods. To do this, the program must consistently use each grid to solve the corresponding problem with each of the methods specified in the task variant.
When solving a problem, the program must measure the parameters of the algorithm: the total time of calculations (excluding the time spent on input / output of results), the number of algorithm steps performed, the error of the result of solving the problem. These are
The results should be presented in the form of a table and a graph as a dependency on the length of the segment - for each of the implemented methods, each of the selected "test" equations / systems. The student should draw a conclusion about the nature of the dependencies and compare them with analytical data. This data is also required
To draw a conclusion about the comparative effectiveness of the methods implemented in the program.
Option: Method comparison: the explicit-implicit three-step Adams scheme (for acceleration, the three-stage Runge-Kutta scheme) and the explicitly implicit Euler method.
It is one or more functions; for each function it is necessary (on the same graphical plane) to construct two graphs – obtained by experiment and “theoretical” – obtained from a pre-known analytical representation of this desired function. The method of conducting the experiment, therefore, consists in the fact that a certain equation or system is fixed, the solution of which is known in advance (obtained analytically by hand), and this solution is compared with the result of the work of numerical algorithms.
For an analytically defined function on a segment, make a series of grids of 100, 150, . . 600 knots. Each grid should be with equidistant or unequal nodes - depending on the specifics of the method specified in the option. If the task indicates two (or more) methods, or a family of methods (in particular, standard formulas (for example, the formulas of Newton, Stirling or Bessel) set a family of similar methods of different order), you need to perform a comparison of the effectiveness of the method.
These methods. To do this, the program must consistently use each grid to solve the corresponding problem with each of the methods specified in the task variant.
When solving a problem, the program must measure the parameters of the algorithm: the total time of calculations (excluding the time spent on input / output of results), the number of algorithm steps performed, the error of the result of solving the problem. These are
The results should be presented in the form of a table and a graph as a dependency on the length of the segment - for each of the implemented methods, each of the selected "test" equations / systems. The student should draw a conclusion about the nature of the dependencies and compare them with analytical data. This data is also required
To draw a conclusion about the comparative effectiveness of the methods implemented in the program.
Option: Method comparison: the explicit-implicit three-step Adams scheme (for acceleration, the three-stage Runge-Kutta scheme) and the explicitly implicit Euler method.
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