Application of Mohan Transform in Initial and Boundary Value Problems

Abstract: This paper presents the application of the Mohan transform for solving initial value problems and boundary value problems arising in ordinary and partial differential equations. The study demonstrates that the Mohan transform is an efficient analytical tool for converting differential equations into simpler algebraic forms, thereby reducing computational complexity and simplifying solution procedures. Fundamental properties of the Mohan transform, including linearity, derivative transforms, and convolution properties, are discussed and utilized in the formulation of solutions. Several numerical illustrations involving homogeneous and non-homogeneous boundary value problems, heat equations, and wave equations are solved systematically using the transform technique. Graphical comparisons and error analysis confirm that the Mohan transform produces exact or near-exact solutions comparable to those obtained by the Laplace transform while requiring fewer computational steps. The results establish that the Mohan transform is a reliable and powerful mathematical approach for solving a wide class of engineering, physics, and applied mathematics problems.

Keywords: Mohan Transform, Initial Value Problems, Boundary Value Problems, Partial Differential Equations, Integral Transform, Numerical Illustration, Exact Solution, Laplace Transform Comparison.