t

x

$\alpha =0.2$

$\alpha =0.7$

$\alpha =1$

Exact Solution

Abs. error $\left|u_{Exact}-u_{LDM}\right|$

0.1

0.5

0.55330756

1.0548937

1.2014201

1.2012147

0.00020536966

1.0

0.71046097

1.3545103

1.542654

1.5423903

0.00026369986

1.5

0.91224994

1.7392257

1.9808069

1.9804683

0.00033859733

2.0

1.1713521

2.23321

2.5434064

2.5429716

0.00043476757

0.5

0.5

0.78942785

0.83412887

0.91975844

0.92004441

0.00028597406

1.0

1.0136454

1.0710427

1.1809932

1.1813604

0.00036719796

1.5

1.3015465

1.375246

1.5164253

1.5168968

0.00047149152

2.0

1.6712188

1.7658508

1.9471286

1.94773404

0.00060540709

0.9

0.5

0.78469782

0.7174914

0.70407427

0.70468809

0.00061381852

1.0

1.0075719

0.92127719

0.90404926

0.90483742

0.00078815858

1.5

1.293748

1.1829433

1.1608222

1.1618342

0.0010120157

2.0

1.6612053

1.5189293

1.4905252

1.4918247

0.0012994538