New development of homotopy analysis method for non-linear integro-differential equations with initial value problems

Homotopy analysis method (HAM) was proposed by Liao in 1992 in his PhD thesis for non-linear problems and was applied in many different problems of mathematical physics and engineering.  In this note, a new development of homotopy analysis method (ND-HAM) is demonstrated for non-linear integro-differential equation (NIDEs) with initial conditions.  Practical investigations revealed that ND-HAM leads an easy way how to find initial guess and it approaches the exact solution faster than the standard HAM, modified HAM (MHAM), new modified of HAM (mHAM) and more general method of HAM (q-HAM). 

Технологія перетворення п’ятимовного словника порівнянь у електронну форму

In this article the structure of Ukrainian-Russian-Belarusian-Polish dictionary of comparisons was analyzed and the technology of its transformation from paper into electronic form was proposed.
 Key words: lexicography, dictionary