In this study, we developed a solution of nonhomogeneous heat equation with Dirichlet boundary conditions. moreover, the non-homogeneous heat equation with constant coefficient. since heat equation has a simple form, we would like to start from the heat equation to find the exact solution of the partial differential equation with constant coefficient. to emphasize our main results, we also consider some important way of solving of partial differential equation specially solving heat equation with Dirichlet boundary conditions. the main results of our paper are quite general in nature and yield some interesting solution of non-homogeneous heat equation with Dirichlet boundary conditions and it is used for problems of mathematical modeling and mathematical physics.
The study examined the use of population spectrum in determining the nature (deterministic and stochastic) of trend and seasonal component of given time series. It also adopts the use of coefficient of variation approach in the choice of appropriate model in descriptive time series technique. Illustrations were carried out using average monthly atmospheric Carbon dioxide (C02) from 2000-2017 with 2018 used for forecast. Spectrum analysis showed that the descriptive technique of time series is more appropriate for analysis of the study data. The coefficient of variation revealed that the multiplicative model was appropriate for the CO2 data while the forecast and the actual values showed no significant mean difference at 5% level of significance.
The stabilizing optimal feedback is a function onthe separatrix of stable points of the associated Hamiltoniansystem. Three geometric objects - the symplectic form, Hamiltonianvector field, and Lyapunov function, generating the separatrix - are %intrinsic to the optimal control system. They areinvariantly attached to the optimal control system under canonicaltransformations of the phase space. The separatrix equations can be writtenin terms of these invariants through invariant operations.There is a computable representative of the equivalence class,containing the original system. It is its linear approximation system at the stable point.
The aim of this article is to calculate the soliton solutions of space-time fractional-order modified extended Zakharov-Kuznetsov equation which is modeled to investigate the waves in magnetized plasma physics. Fractional derivatives in the form of modified Riemann-Liouville derivatives are used. Complex fractional transformation is applied to convert the original nonlinear partial differential equation into another nonlinear ordinary differential equation. Then, soliton solutions are obtained by using (1/G')-expansion method. Bright and dark soliton solutions are also obtain with ansatz method. These solutions may be of significant importance in plasma physics where this equation is modeled for some special physical phenomenon.
We apply Ablowitz-Kaup-Newel-Segur hierarchy to derive the generalized shallow waterwave equation and we also investigate N-soliton solutions of the derived equation using InverseScattering Transform method and Hirota’s bilinear method.
