New Wave Solutions for Nonlinear Differential Equations using an Extended Bernoulli Equation as a New Expansion Method

In this paper, we presented a new expansion method constructed by taking inspiration for the Kudryashov method. Bernoulli equation is chosen in the form of F′=BFn-AF and some expansions are made on the auxiliary Bernoulli equation which is used in this method. In this auxiliary Bernoulli equation some wave solutions are obtained from the shallow water wave equation system in the general form of “n-order”. The obtained new results are simulated by graphically in 3D and 2D. To sum up, it is considered that this method can be applied to the several of nonlinear evolution equations in mathematics physics

Al-Khwârizmî's Place and Importance in the History of Mathematics

The aim of this study is to introduce Muḥammad ibn Mûsâ al-Khwârizmî and his works in terms of history of mathematics and mathematics education. Muḥammad ibn Musa al-Khwârizmî an Iraqi Muslim scholar and it is the first of the Muslim mathematicians who have contributed to this field by taking an important role in the progress of mathematics in his own period. He found the concept of Algorithm in mathematics. In some circles, he was given the nickname Abu Ilmi’l-Hâsûb (the father of the account). He carried out important studies in algebra, triangle, astronomy, geography and map drawing. Algebra has carried out systematic and logical studies on the solution of inequalities at second level in the development of the algebra. He with all these studies have contributed to mathematical science and today was a guide to the works done in the field of mathematics

New Wave Solutions for Nonlinear Differential Equations using an Extended Bernoulli Equation as a New Expansion Method

In this paper, we presented a new expansion method constructed by taking inspiration for the Kudryashov method. Bernoulli equation is chosen in the form of F′=BFn-AF and some expansions are made on the auxiliary Bernoulli equation which is used in this method. In this auxiliary Bernoulli equation some wave solutions are obtained from the shallow water wave equation system in the general form of “n-order”. The obtained new results are simulated by graphically in 3D and 2D. To sum up, it is considered that this method can be applied to the several of nonlinear evolution equations in mathematics physics

Al-Khwârizmî's Place and Importance in the History of Mathematics

The aim of this study is to introduce Muḥammad ibn Mûsâ al-Khwârizmî and his works in terms of history of mathematics and mathematics education. Muḥammad ibn Musa al-Khwârizmî an Iraqi Muslim scholar and it is the first of the Muslim mathematicians who have contributed to this field by taking an important role in the progress of mathematics in his own period. He found the concept of Algorithm in mathematics. In some circles, he was given the nickname Abu Ilmi’l-Hâsûb (the father of the account). He carried out important studies in algebra, triangle, astronomy, geography and map drawing. Algebra has carried out systematic and logical studies on the solution of inequalities at second level in the development of the algebra. He with all these studies have contributed to mathematical science and today was a guide to the works done in the field of mathematics

Novel Exact Solutions of the Extended Shallow Water Wave and the Fokas Equations

In this study, a Sine-Gordon expansion method for obtaining novel exact solutions of extended shallow water wave equation and Fokas equation is presented. All of the equations which are under consideration consist of three or four variable. In this method, first of all, partial differential equations are reduced to ordinary differential equations by the help of variable change called as travelling wave transformation, then Sine Gordon expansion method allows us to obtain new exact solutions defined as in terms of hyperbolic trig functions of considered equations. The newly obtained results showed that the method is successful and applicable and can be extended to a wide class of nonlinear partial differential equations