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01-Applied Mathematics & Information Sciences
An International Journal


Volumes > Volume 10 > No. 5


A New Numerical Approach for the Solutions of Partial Differential Equations in Three-Dimensional Space

PP: 1663-1672
Brajesh Kumar Singh, Carlo Bianca,
This paper deals with the numerical computation of the solutions of nonlinear partial differential equations in threedimensional space subjected to boundary and initial conditions. Specifically, the modified cubic B-spline differential quadrature method is proposed where the cubic B-splines are employed as a set of basis functions in the differential quadrature method. The method transforms the three-dimensional nonlinear partial differential equation into a system of ordinary differential equations which is solved by considering an optimal five stage and fourth-order strong stability preserving Runge-Kutta scheme. The stability region of the numerical method is investigated and the accuracy and efficiency of the method are shown by means of three test problems: the threedimensional space telegraph equation, the Van der Pol nonlinear wave equation and the dissipative wave equation. The results show that the numerical solution is in good agreement with the exact solution. Finally the comparison with the numerical solution obtained with some numerical methods proposed in the pertinent literature is performed.

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