Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

高等学校計算数学学報 = Numerical mathematics

The mathematical model for many problems is arising in different industries of natural science, basically formulated using differential, integral and integro-differential equations. The investigation of these equations is conducted with the help of numerical integration theory. It is commonly known that a class of problems can be solved by applying numerical integration. The construction of the quadrature formula has a direct relation with the computation of definite integrals. The theory of definite integrals is used in geometry, physics, mechanics and in other related subjects of science. In this work, the existence and uniqueness of the solution of above-mentioned equations are investigated. By this way, the domain has been defined in which the solution of these problems is equivalent. All proposed four problems can be solved using one and the same methods. We define some domains in which the solution of one of these problems is also the solution of the other problems. Some stable methods with the degree p<=8 are constructed to solve some problems, and obtained results are compared with other known methods. In addition, symmetric methods are constructed for comparing them with other well-known methods in some symmetric and asymmetric mathematical problems. Some of our constructed methods are compared with Gauss methods. In addition, symmetric methods are constructed for comparing them with other well-known methods in some symmetric and asymmetric mathematical problems. Some of our constructed methods are compared with Gauss methods. On the intersection of multistep and hybrid methods have been constructed multistep methods and have been proved that these methods are more exact than others. And also has been shown that, hybrid methods constructed here are more exact than Gauss methods. Noted that constructed here hybrid methods preserves the properties of the Gauss method.

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Novel Symmetric Numerical Methods for Solving Symmetric Mathematical Problems

Some refinement of the notion of symmetry for the Volterra integral equations and the construction of symmetrical methods to solve them

A new computational approach to the fractional-order Liouville equation arising from mechanics of water waves and meteorological forecasts

On one application of forward jumping methods

On some comparison of multistep second derivative methods with the multistep hybrid methods and their application to solve integro-differiential equations

Solving of integro-differential equations with variable boundaries encounters in many areas of natural science. Numerous articles and monographs are published on the qualitative theory and numerical methods for solving such equations. However, among these works there are almost no papers on the determination of the stability of numerical methods. Therefore, here a test equationis constructed, and it is applied to the studyof the stability region of hybrid methods with the order of accuracy. For the constructedmodel equations the above mentioned methodsare compared with the known.

G.Yu. Mehdiyeva

Papers

Novel Symmetric Numerical Methods for Solving Symmetric Mathematical Problems

Some refinement of the notion of symmetry for the Volterra integral equations and the construction of symmetrical methods to solve them

On one application of forward jumping methods

On some comparison of multistep second derivative methods with the multistep hybrid methods and their application to solve integro-differiential equations

On the application of hybrid methods to solving Volterraintegro-differential equation