Analytic solution of transcendental equations

Analytic solution of transcendental equations

According to the assumption that si = sj for i = j, the matrix (5) has an inverse and the system (2) and (4) can be solved. We denote by V the Vandermonde determinant of the matrix (5) and by Vk the Vandermonde determinant of order (n − 1) of the variables s1, . . . , sk−1, sk+1, . . . , sn. We also denote by Φ r the fundamental symmetric function of the r-th order of (n − 1) variables s1, . . ...

Numerical Solution of Two Transcendental Equations

This paper deals with the study of the transcendental equations: sin(j + v)/(s + v) = ±sin(i v)/(s v), where v = (s2 y2)'/2. These equations are obtained in the study of some boundary value problems for a modified biharmonic equation using the PapkovichFadle series. Some numerical solutions obtained with an iterative procedure are given. Introduction. It is well known that the governing equatio...

Solution of Extreme Transcendental Differential Equations

Extreme transcendental differential equations are found in many applications including geophysical climate change models. Solution of these systems in continuous time has only been feasible with the recent development of Runge−Kutta sampling transcendental differential equation solvers with Chebyshev function output such as Mathematica 9÷s NDSolve function. This paper presents the challenges an...

F 9 The solution of transcendental equations

O u r c h a p t e r c o n c e r n s t h e a p p r o x i m a t i o n of a zero off(x) o r , equ iva len t ly , t h e a p p r o x i m a t i o n pf a r o o t o f t h e e q u a t i o n f(x) = 0 b y i te ra t ive m e t h o d s . W e shal l t a k e / as t r a n s c e n d e n t a l a l t h o u g h t h e m e t h o d s w e discuss c a n a lso b e u s e d if / is a p o l y n o m i a l . I f w e use these...

On the analytical solution of some families of transcendental equations