Introduction of Novel Operational Matrices, may be modified to examine the solution to more diverse problems of a physical nature in intricate geometries. Research was conducted to verify the consistency and aid the mathematical structure […]
Frobenius Method, we consider the general second order linear differential equation, (9.1) and attempt to solve it about a regular singular point . For that, we employ the Frobenius method as illustrated in […]
The Fourier Transform ,we move on in our program of decomposing arbitrary functions into sinusoids. We have seen how a periodic function can be expressed as a Fourier series, so now we seek a similar […]
Continuity, most of the functions we study in elementary calculus are described by simple formulas. These functions almost always possess derivatives and, in fact, a portion of any first course in calculus is devoted to […]
Initial Value Problems are solved using the Laplace Transform Method, as mentioned earlier, the Laplace transform method is very convenient way of solving ordinary differential equations in general and those with constant coefficients in particular. […]
Meixner Wavelet Method,we proposed a new algorithm by inserting Meixner polynomials in traditional Legendre wavelets method. This technique is successively applied to find the exact solution singular ordinary differential equations. The proposed technique is very […]
The Convolution Theorem, we know that the Laplace transform of a sum of two functions is the sum of the transforms of those functions, i.e., On the same analogy we may think of a similar […]
Dirac Delta Function , the unit step function (or the Heaviside function) helps us in solving differential equations with discontinuous forcing functions. However, there are many problems in Electrical/Mechanical/Mechatronics/Civil Engineering and Physics which involve impulsive […]
Applications of Gegenbauer Polynomials Method,we develop a new algorithm for solving linear and nonlinear integral equations using Galerkin weighted residual numerical method with Gegenbauer polynomials. Gegenbauer polynomials [1] is given as (3.96) , . […]
Laplace Transforms acquired a new importance when the English Electrical Engineer Oliver Heaviside(1850-1925 AD) made use of them in operational calculus(devised by him) and for the solution of ordinary differential equations with constant coefficients. The […]
