Solving Linear Boundary Value Problems Using Maples dsolve Command

6 Solving Linear Boundary Value Problems Using Maple s dsolve Command 

Maple s dsolve command can be used to solve linear boundary value problems. One of the advantages of using Maple s dsolve command is Maple can give Bessel and other special function solutions to linear boundary value problems. However, the analytical solution obtained from the dsolve command may not be in simplified or elegant form. The syntax for using the dsolve command is follows. 

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In section 3.1.6, linear Boundary value problems were solved using Maple s dsolve command. The solution obtained may not be in the simplified form. Maple gives the Bessel function and other special function solutions for linear... 

In this chapter, analytical solutions were obtained for parabolic and elliptic partial differential equations in semi-infinite domains. In section 4.2, the given linear parabolic partial differential equations were converted to an ordinary differential equation boundary value problem in the Laplace domain. The dependent variable was then solved in the Laplace domain using Maple s dsolve command. The solution obtained in the Laplace domain was then converted to the time domain using Maple s inverse Laplace transform technique. Maple is not capable of inverting complicated functions. Two such examples were illustrated in section 4.3. As shown in section 4.3, even when Maple fails, one can arrive at the transient solution by simplifying the integrals using standard Laplace transform formulae. 

The numerical method of lines was used to solve linear and nonlinear elliptic partial differential equations in section 6.1.7. This method involves using finite differences in one direction and solving the resulting system of boundary value problems in y using Maple s dsolve numeric command. This method provides a numerical solution for both the dependent variables and its derivative in the y-direction. 

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