Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this work,  investigate numerically the classical Burgers–Fisher equation using a modified Bhattacharya method. The partial differential equation under investigation possesses nonnegative and bounded solutions and, under some suitable parameter conditions, these solutions are traveling waves. It is ll known that the use of the Bhattacharya approach leads to the design of numerical techniques that are sensitive to zero solutions. Hover, in this manuscript,  provide a correction of that technique in order to approximate solutions of the Burgers–Fisher equation that are bounded in   [0,1]      [  0  ,  1  ]        . The proposed methodology is explicit, and  establish thoroughly the capability of the technique to preserve the non-negativity, the boundedness and the monotonicity of the numerical approximations, as ll as the constant solutions of the continuous model. The new class of methods introduced in this work considers the presence of a free parameter, and  show that this family tends to an explicit and standard discretization of the Burgers–Fisher equation when the free parameter tends to infinity. Some simulations illustrate the main features of the method.
['Jorge Eduardo Macías-Díaz', 'Armando Gallegos', 'H. Vargas-Rodríguez']
I am writing a research paper on a idea A modified Bhattacharya exponential method to approximate positive and bounded solutions of the Burgers–Fisher equation
[{"from": "human", "value": "I am writing a research paper on a idea A modified Bhattacharya exponential method to approximate positive and bounded solutions of the Burgers\u2013Fisher equation"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this work,  investigate numerically the classical Burgers\u2013Fisher equation using a modified Bhattacharya method. The partial differential equation under investigation possesses nonnegative and bounded solutions and, under some suitable parameter conditions, these solutions are traveling waves. It is ll known that the use of the Bhattacharya approach leads to the design of numerical techniques that are sensitive to zero solutions. Hover, in this manuscript,  provide a correction of that technique in order to approximate solutions of the Burgers\u2013Fisher equation that are bounded in   [0,1]      [  0  ,  1  ]        . The proposed methodology is explicit, and  establish thoroughly the capability of the technique to preserve the non-negativity, the boundedness and the monotonicity of the numerical approximations, as ll as the constant solutions of the continuous model. The new class of methods introduced in this work considers the presence of a free parameter, and  show that this family tends to an explicit and standard discretization of the Burgers\u2013Fisher equation when the free parameter tends to infinity. Some simulations illustrate the main features of the method."}]