TY  - Type of reference 
TI  - Series solution method for the reaction-diffusion equation over finite intervals 
AU  - Edoh Tossou
 
AU  - Kwassi Anani
 
AU  - Roger Prud’homme 
AB  - This paper makes a contribution by generalizing the classical series solution for initial boundary value problems of the one-dimensional reaction-diffusion equation on any finite interval of the real line. The general form of the equation is considered on a generic bounded interval and is subjected in the unified way to the three classical boundary conditions, namely the Neumann, Dirichlet, and Robin boundary conditions. The Fourier decomposition method, is used to derive the solution of the resulting homogeneous equation with zero boundary conditions. Subsequently, the solution of the nonhomogeneous equation with homogeneous boundary conditions is obtained using the Duhamel’s principle. Finally, the solution of the general problem is obtained as a convergent series over the considered interval, with the construction of an auxiliary. The Hopf-Cole transformation has facilitated the generalization of the exact solution of the Burger’s equation to generic intervals, as demonstrated by the described method. 
DO  - 10.21494/ISTE.OP.2024.1191 
JF  - Thermodynamics of Interfaces and Fluid Mechanics 
KW  - Heat transfer, Duhamel principle, Sturm-Liouville theory, Fourier decomposition method, Burgers equation, Transfert de chaleur, Principe de Duhamel, Théorie de Sturm-Liouville, Méthode de décomposition de Fourier, Equation de Burgers,  
L1  - https://openscience.fr/IMG/pdf/iste_timf24v7n1_1.pdf 
LA  - en 
PB  - ISTE OpenScience 
DA  - 2024/08/9 
SN  - 2514-4642 
TT  - Méthode de solution en série pour l’équation de réaction-diffusion sur les intervalles finis 
UR  - https://openscience.fr/Series-solution-method-for-the-reaction-diffusion-equation-over-finite-intervals 
IS  - Issue 1 
VL  - 7 
ER  -