Application of a boundary-only meshfree method for time-dependent problems

The boundary knot technique is an integration free, boundary-only, meshless method which is used to avoid the known disadvantages of the method of fundamental solution. But, in original form, the boundary knot method can not be implemented for parabolic problems. One way to overcome this disadvantage is employing the analog equation method. According to analog equation method, the nonlinear governing operator is replaced by an equivalent nonhomogeneous linear one with known fundamental solution and under the same boundary conditions.